Old English Scottas (plural) "inhabitants of Ireland, Irishmen," from Late Latin Scotti (c. 400), a name of uncertain origin, perhaps from Celtic (but answering to no known tribal name; Irish Scots appears to be a Latin borrowing). The name followed the Irish tribe which invaded Scotland 6c. C.E. after the Romans withdrew from Britain, and after the time of Alfred the Great the Old English word described only the Irish who had settled in the northwest of Britain.

"of Scotland," 1590s, a contraction of Scottish. As a noun, by 1743 as "the people of Scotland collectively;" 1700 as "the sort of English spoken by the people of Scotland." 

Scots (mid-14c.) is the older adjective, which is from Scottis, the northern variant of Scottish. Scots was used in Scottish English until 18c., then Scotch became vernacular, but in mid-19c. there was a reaction against it because of insulting and pejorative formations made from it by the English (such as Scotch greys "lice;" Scotch attorney, a Jamaica term from 1864 for strangler vines).

Scotch-Irish is from 1744 (adj.); 1789 (n.); more properly Scots-Irish (1966). Commercial Scotch Tape (1945) was said to be so called because at first it had adhesive only on the edges (to make it easier to remove as a masking tape in car paint jobs), which was interpreted as a sign of cheapness on the part of the manufacturers. It had become a verb by 1955 and for a time was often printed without capitals.

"Scottish, of or relating to Scotland or its inhabitants," mid-14c., a contracted variant of Middle English Scottis, a northern dialectal form of Scottish. Also compare Scotch. As "the dialect of English spoken in the Scottish lowlands," by 1540s.