Left wing=liberal
Right wing=conservative
These are common usages of the terms. Finer gradations may occur to express how left or right something is, but it's still left and right.
Yet early Conservatives described themselves as liberal? I am most confused.
In the classical sense Liberals tend to break from the norm. In the days of ancient Greece, a self-ruling society would have been the odd man out amongst monarchies and such. A government designed to keep power in the hands of the governed would have been a most liberal idea in such an environment.
Conservatives however tended to be for the status quo.
With the advent of a Constitutional Republic the status quo became individual rights and freedoms; a change that made Conservatives (supporting the status quo) the champion and Liberals the ones wanting change.
Look back at the Republican fight against slavery, Jim Crowe, etc.; pretty liberal in those times. More recently (JFK - ask not what your country can do for you) the Democrats would have sounded like modern Republicans.
Left and Right were terms based on where each party sat within the Congress and Senate chambers and got associated in media along the way with L/C ideology in a more fixed way than party malleability.
Mid 20th century we experienced what Ike warned us about in his final speech to the nation; the Military/Industrial/(Lobbyist) Complex and it's corrupting influence over our representatives. Today, few (regardless of party affiliation) mean what they say when pandering to audiences and are all for the status quo within the confines of keeping each person in office and each party in primary or secondary power so they exempt themselves from onerousness laws and taxation while amassing personal wealth and expanding government power over the Governed (because that further cements the power and wealth for themselves and their croneys).