The adjectives associated with the nouns Eng. language and Sp. lengua and lenguaje are no other than the learned words Eng. linguistic and Sp. lingüístico/a, which mean either ‘of or pertaining to language or languages’ or ‘of or pertaining to the knowledge or study of languages’ (OED), as in linguistic diversity (Sp. diversidad lingüística), linguistic heritage (Sp. patrimonio lingüístico). English, of course, has the option of using the noun language as a modifier in a noun-noun construction (compound noun) as an alternative to the use of this adjective, thus resulting in the synonymous phrases language diversity and language heritage (cf. Part I, Chapter 5, §5.8). Spanish can only turn a noun into a modifier by resorting to a prepositional phrase, with a linking preposition, typically de ‘of’, as in diversidad de lenguas and patrimonio de lenguas.
The source of Eng. linguistic and Sp. lingüístico/a is not a Classical Latin word, but rather the New Latin adjective linguisticus, derived from the noun linguista with the addition of the Latin adjectival suffix ‑ic‑ (lingu‑ist‑ic‑us). Latin did have an adjective derived from the noun lĭngua ‘language’, by means of the adjectival suffix ‑āl‑, namely linguālis, but the meaning of this adjective was ‘of or related to the tongue’, referring to the organ, not to the other sense of the noun lingua, namely ‘language’ (lingu‑āl‑is). Actually, both English and Spanish have borrowed the (rare) adjective lingual from Latin, with the meaning is ‘of or relating to the tongue’, and used mostly as a technical word, as in (in anatomy) lingual nerve (Sp. nervio lingual), i.e. the nerve of the tongue, and (in linguistics) lingual sounds (Sp. sonidos linguales), that is, sounds made with the tongue. The word lingual has been used in the past with the ‘of or relating to language’ sense, but that use is now archaic, if not obsolete. In other words, while looking for a Latinate adjective that meant ‘of or relating to language’, the English, Spanish, and French have all resorted to the newly formed adjective linguistic (Sp. lingüístico/a) derived from the New Latin word linguist (Sp. lingüista).
This adjective in question first appeared in French, as linguistique, in 1826, from the New Latin adjective linguisticus (fem. linguistica, neut. linguisticum). The French adjective linguistique [lɛ̃.ɡɥis.ˈtik] was derived from the noun linguiste [lɛ̃.ˈɡɥist], which is first attested in French about two hundred years earlier, around 1632, though this French noun was very rare until the adjective linguistique was created. The noun linguiste was created out of the noun lingua and the Latin agentive suffix ‑ist‑, of Greek origin. This noun was originally used in French with the meaning ‘someone who studied ancient languages’. It wasn’t until the 20th century that it came to mean ‘someone who studies modern languages scientifically’, though in the 19th century it was used sometimes as a synonym for philologist, someone who studies languages from a comparative and historical perspective.
It is not clear when and where the words Eng. linguist or Fr. linguiste started to be used. We find Eng. linguist already in use in English in the late 16th century, decades before it is attested in French. The early meanings linguist in English were: (1) ‘one who uses his tongue freely or knows how to talk; a master of language’ and (2) ‘one who is skilled in the use of languages; one who is master of other tongues besides his own’ (OED). To this day, the word linguist in English is used with the latter of the two original senses, as well as with the sense it acquired in more recent times, namely ‘someone who studies language and languages scientifically’, i.e. a practitioner of linguistics.
Although the noun linguist may have been created in English, the adjective linguistic on the other hand, is said to have had its origin in French, being derived from the noun linguiste, as we said earlier, by the year 1826. Actually, the word may have been modelled on the German word linguistisch that meant ‘of or relating to the academic study of language’ which is first attested in the previous century, in 1787. In the 20th century, Ger. linguistisch has also come to mean ‘of or relating to language’ in addition to ‘of or relating to linguistics’, like its cognate in the other European languages and as an alternative to the native sprachlich. The German adjective linguistisch was derived from the German word Linguistik, which was created in 1778 for the name of the study of language, which at the time meant the study of the history of language (historical linguistics). (Curiously, in modern-day German, the common term for ‘linguistics’ is not Linguistik but Sprachwissenschaft. The non-Latinate adjective synonym of the ‘of or relating to linguistics’ of Ger. linguistisch is, thus, sprachwissenschaftlich.)
The name for the academic discipline that studies language scientifically is linguistics in English. This word is typically said to have come about in French, as a noun identical to the adjective linguistique that we just mentioned above. The OED, for example, gives that as the source of the term. Originally, in the 19th century (after 1835 at least) it was used with the sense of comparative and historical linguistics. By a hundred years later, as the scientific discipline of language changed, linguistique came to be associated with this new science, whose main exponents were Whitney and Saussure. It would seem, however, that French calqued this word from the German Linguistik that we have mentioned is attested in the late 18th century, a Latinate word derived from Linguist by means of the suffix ‑ik, the German version of the Latin adjectival suffix ‑ic, used to name academic disciplines, such as Physik ‘physics’ or Mathematik ‘mathematics’.
The French term linguistique was calqued into English as linguistics [lɪŋ.ˈɡwɪ.stɪks] and into Spanish lingüística [liŋ.ˈɡu̯is.t̪i.ka]. Notice that the English noun linguistics looks formally like a plural, formed by analogy with the names of other academic disciplines in English that end in ‑ics, such as physics, mathematics, economics, athletics, physics, statistics, genetics, pediatrics, phonetics, robotics, politics, etc. These are, however, singular nouns, as the fact that they go with singular verb forms. Thus, we say, for example, Linguistics is a science, not *Linguistics are a science. However, originally these names did behave as plural nouns, not as singular ones as they do today, so in earlier times, one would say Physics are difficult, not Phisics is difficult.
The tradition of making the names of disciplines plural started in English in the 16th century as a revival of the Classical Greek custom of using the neuter plural of adjectives with the meaning ‘matters relevant to’ in matters related to academic fields of study. Names of disciplines that were common before the 16th century, however, remain in the singular, such as arithmetic and logic. However, mathematics has always been plural, and this is probably due to the fact that originally this field was not thought of as a single thing, but as ‘the collective name for geometry, arithmetic, and certain physical sciences (as astronomy and optics) involving geometrical reasoning’ (OED).
With the exception of matemáticas ‘mathematics’, the names of disciplines in Spanish are always singular, and feminine, just like in French, derived from the same adjectival suffix ‑ic‑, resulting in the ending ‑ic‑a. Thus, the Spanish equivalent of Eng. linguistics, is lingüística, identical to the feminine singular form of the adjective we just mentioned. Thus, Sp. lingüística works just like the names of other disciplines that end in ‑ica, such as (la) física ‘physics’ and (la) estadística ‘statistics’, and (la) genética, (la) robótica, (la) fonética, (la) política, etc., which are also singular and identical in form to the feminine form of the related adjectives. For example, física, the name of the discipline, is homonymous with the feminine adjective física meaning ‘physical’ (the masculine singular form of this adjective is físico and the plural forms would be físicas and físicos, respectively. Note that to confuse things even further, besides being an adjective, físico can also be a noun, meaning ‘physicist’. As we said, an exception to this singular form of academic disciplines is (las) matemáticas, which is plural (it ends in ‑icas, not ‑ica). Note that unlike Eng. mathematics, Sp. matemáticas is a real plural, since we say, for example, Las matemáticas son difíciles, with a plural article, a plural verb form, and a plural adjective. In North America, the name mathematics is colloquially shortened to math, whereas in Great Britain, can also be reduced to maths, especially when referring to the subject studied at school (1911).
 The word heritage typically translates as Sp. patrimonio, especially if it is the heritage of a group or nation. The word herencia, a paronym of heritage, can also be used when speaking of the heritage of an individual. Note that the word herencia can also mean ‘inheritance’. Learned Sp. herencia comes from Lat. haerĕntĭa ‘things attached, things that cling’ or ‘belongings’, a noun derived from the regular stem haerĕnt‑ of the present participle haerens ‘clinging, adhering’ of the verb haerēre (supine haesum) ‘to cling, adhere’. Eng. heritage comes from Old French heritage ‘inheritance’, derived by means of the suffix ‑age from heriter ‘inherit’, from Late Latin hereditare. Old Spanish had the cognate heredaje and it still has the verb heredar ‘to inherit’ derived from the same Late Latin verb. Eng. inherit comes from Old French enheriter ‘appoint as heir’, from Late Latin inhereditare ‘to appoint as heir’, a prefixed version of hereditare.
 Note that not all the recently created English words for discipline names that end in ‑ics have equivalent words in Spanish that end in ‑ica. For example, pediatrics (1884) translates as pediatría, a word with the same stem but with a different Greek suffix. Likewise, gymnastics (1650s) translates into Spanish as gimnasia. The noun athletics (1730), which is thought to have been modelled on the noun gymnastics, translates into Spanish as deportes, if it refers to active sports, a sense that is common in North America for this word, and as atletismo, if it refers to track and field, a sense common in British English. Another such word is acrobatics (1859), whichi translates as acrobacia.