Eng. respire ~ Sp. respirar
Lat. respīrāre was formed with the prefix re‑ ‘back; again’ and thus originally meant literally ‘to blow or breathe back’ and ‘to breathe out, exhale’ (L&S) though, by extension, it also came to mean, more generally ‘to breathe’. That latter meaning is the main one that this word’s descendant has in Spanish, namely ‘to breathe’, as in the process of ‘tak[ing] air into the lungs and then expel it as a regular physiological process’ (COED). Other neighboring Romance languages also have cognates of this word as the word meaning ‘to breathe’, e.g. Catalan/Portuguese respirar, Fr. respirer, It. respirare.
Curiously, English too has a cognate of Sp. respirar, and with the exact same meaning. However, Eng. respire is very fancy and rare synonym of the English native verb to breathe. It seems it was borrowed from written Latin as well as from Old French at different times around the late 14th century. The verb, again, is not at all common, though some words derived from it are quite common. The derived noun, respiration, for example, is common. It refers to ‘the action of breathing’, although in biology it has a more technical meaning, namely ‘the processes in living organisms involving the production of energy, typically with the intake of oxygen and the release of carbon dioxide, from the oxidation of organic substances’ (COED). This noun’s Spanish cognate is respiración, which translates both as breathing and as respiration. A common collocation containing the word respiration in English is artificial respiration, which refers to ‘a procedure used to restore or maintain respiration in a person who has stopped breathing [using] mechanical or manual means to force air into and out of the lungs in a rhythmic fashion’ (AHD) (Sp. respiración artificial).
Also common in English is the agentive derived noun respirator, which can refer to a machine used in artificial respiration, that is, ‘a piece of equipment that pumps air in and out of someone’s lungs if they are too ill or weak to breathe’ (DOCE). Other names for this type of machine are ventilator and inhalator. The Spanish name for such a medical machine is, not surprisingly, respirador. Note, however, that the English word respirator is also used sometimes as equivalent of gas mask, namely ‘a piece of equipment that you wear over your nose and mouth to help you breathe in a place where there is harmful gas, smoke etc.’ (DOCE). That sense of the word translates into Spanish as máscara antigás or mascara de oxígeno. The word respirator first appears in English for such devices in the 18th century, around the same time its French equivalent cognate respirateur is attested. Sp. respirador is no doubt a loanword from one of those two languages.
There are cognate adjectives related to this noun, namely Eng. respiratory ~ Sp. respiratorio. Their meaning is ‘relating to or affecting respiration or the organs of respiration’. They both come from Modern Latin respiratorius, probably through French respiratoire, which was borrowed first. This Modern Latin noun was formed from the adjectival ‑ōr‑ĭ‑ suffix (‑ōrĭus, ‑ōrĭa, ‑ōrĭum) that is the source of the English Latinate suffix ‑ory. This Latin suffix was attached to agentive nouns created with the suffix ‑ōr‑ to form adjectives that expressed a quality associated with the action performed by an agent, such as in this case respirator.
One more word that is related to the verb respirar in Spanish is the noun respiro, which can mean ‘(the action and result of) breathing, breath’, but mostly is used figuratively with the sense of ‘breather, break’ (cf. Sp. reposo, descanso), ‘relief’, ‘respite’, or ‘breathing space’. Two common phrases containing this noun are no dar respiro ‘to give no peace, give no respite’ and tomarse un respiro ‘to take a breather’ (VOX).
 Note that since the ‑ōr‑ ending attached to the stems of passive participles, which typically ended in t, we sometimes think of the English reflex of this suffix as being ‑tory, not ‑ory.) Eventually, some adjectives with this suffix came to be used as nouns associated with a place (e.g. laboratory, observatory) or an instrument associated with the action. These nouns were derived from the neuter form ‑ōrĭum of the adjective.