Liberty, broadly speaking, is the freedom to do as one pleases so long as one doesn't violate anyone else's right to do likewise.
Liberacy, as I understand it (which is not very well, as the term is so infrequently used as to not have a clear definition), is a system of government more commonly known as a
night-watchman state, in which the government's sole function is to provide police and military protection and arbitrate disputes.