good-by

Good-by, Good-bye, n. or interj.

Etymology: [A contraction of God be with ye (God be wî ye, God bw' ye, God bwye).]

Farewell; a form of address used at parting. See the last Note under By, prep. Shak.

Shades of meaning

Fernald has no entry of its own for good-by; he lists it under farewell.

Where he writes about it:

Good-by is the homely and hearty, farewell the formal English word at parting. — from farewell

none given