At first sight it looks as if these words are cognates (parallel developments from the same origin, Latin ūnĭcus) in English and Spanish; they are certainly PARONYMS (words which have a similar form).
In fact the English word is a borrowing from French (in which unique is cognate with Spanish único); it was not imported until the beginning of the 17th century and was not fully assimilated into the language until the second half of the 19th century. The Oxford English Dictionary (OED) observes ‘The adjective was not fully naturalized until the second half of the 19th cent., and its use was sometimes deprecated; it was entered in H.J. Todd Johnson’s Dictionary of the English Language (1818) as a foreign word and characterized as “an affected and useless term of modern times”.’
Incoporation into the Romance languages as a cultismo is much earlier than this. Unico is firmly attested from the 13th century, and Sp. único and Fr. unique from about a century later, with a Portuguese attestation of único from the late 15th century. The Romance languages also had forms derived from the inherited Latin word sōlus (Sp. solo, Pg. só and the derived diminutive form sozinho, Fr. seul, It. solo), with which único, etc. competed. In Latin, ūnĭcus distinguished the non-gradable meaning of ‘single, sole’, while sōlus also had the meaning of ‘alone, deserted’, and this also comes to be the basis of the distinction between Sp. único and solo, It. unico and solo and Pg. único and só/sozinho. By contrast, the English meaning is also more restricted, denoting the notion of ‘the only one of its kind, without equal’.
Some contrasting usages in Spanish, English and French are:
|mi único amigo||my only friend||mon seul ami|
|el único libro que no había leído||the only book I hadn’t read||le seul livre que je n’avais pas lu|
|un hijo único||an only child||un fils unique|
|una obra de arte única||a unique work of art||une œuvre d’art unique|