interspecific (adj.)

word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."

A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.

1630s, "having a special quality," from French spécifique and directly from Late Latin specificus "constituting a kind or sort" (in Medieval Latin "specific, particular"), from Latin species "kind, sort" (see species) +  -ficus "making, doing," from combining form of facere "to make." Earlier form was specifical (early 15c.). Meaning "definite, precise" first recorded 1740. Related: Specifically; specificness.

late 14c., in logic, "a class of individuals or things," from Latin species "a particular sort, kind, or type" (opposed to genus), originally "a sight, look, view; outward appearance, shape, form," a derivative of specere "to look at, to see, behold" (from PIE root *spek- "to observe"). In English it is attested from 1550s as "appearance, outward form."

Latin species "a sight; outward appearance" had many extended senses, including "a spectacle; a mental appearance, an idea or notion;" also "semblance, pretext; manner, fashion; display, beauty; a likeness or statue; reputation, honor." Typically it was used in passive senses. Also compare spice (n.).

In Late Latin, in logic and legal language, it acquired the meaning "a special case," especially (as a translation of Greek eidos) "a class included under a higher class; a kind; a sort; a number of individuals having common characteristics peculiar to them." The notion (as Lewis & Short puts it) is "The particular thing among many to which the looks are turned."

The English word is attested from 1560s as "a distinct class (of something) based on common characteristics." The specific use in biological sciences in reference to groups of living things recognizably distinct from all others by their inherited characteristics is from c. 1600. Endangered species is attested by 1964.