Politician "A" wants economic decisions to be made, whenever feasible, in the private marketplace, according to individual choice, and the law of supply and demand. She is more interested in equality of opportunity, than equality of results.
Politician "B" thinks markets should be heavily regulated. If income inequality passes what he considers an unacceptable threshold, he advocates government action to redistribute income.
Some (though not many in present-day America) would call "A" a "liberal". Some would call "B" a "liberal". What gives?
If one traces the words "conservative" and "liberal" back to their root meanings, they turn out not to be antonyms of each other. And over time, their meanings have been twisted in new directions.
"Liberal" derives from the same root as "liberty". So a liberal is an advocate of liberty.
To some, that means liberty from government abuses, such as excessive taxation, imprisonment without due process, restrictions on speech or the press, etc. That's sometimes called "traditional liberal" or "libertarian".
Others argue that an activist government is necessary, in order to provide liberty. Poor people have no liberty to pursue education, or the hallowed "pursuit of happiness" generally, unless government provides them the resources so to do.
And what about "conservative"? From "conserve", i.e., to conserve the status quo. In other words, a conservative is opposed to change.
Therefore, if the status quo is liberal (by whichever definition one chooses), then the conservative is a liberal.
How did our use of these words evolve to reach the current state of things? Stay tuned.