"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.
early 15c., scocchen "to cut, score, gash, make an incision," a word of obscure origin. Century Dictionary considers that it might be a deformation of scratch. Chronology rules out connection with scorch. Perhaps [Barnhart] from Anglo-French escocher, Old French cocher "to notch, nick," from coche "a notch, groove," perhaps from Latin coccum "berry of the scarlet oak," which appears notched, from Greek kokkos.
The meaning "stamp out, crush" (often figurative, of abstract things) is by 1825, earlier "make harmless for a time, wound slightly" (1798), a sense that derives from an uncertain reading of "Macbeth" III.ii.13). Related: Scotched; scotching.
"incision, cut, score, gash," mid-15c., scoch, in cookery, related to scotch (v.). Compare Old French coche "notch on an arrow."