Most Americans are so woefully politically illiterate that they genuinely think "leftist" and "liberal" and "socialism" and "communism" are synonyms.
Left-right is one dimension of ideology.
Liberal-conservative is a completely different dimension.
And, let's be frank, some people have trouble with three. Or two.
This is one reason you should never, ever be a single-issue voter. It makes you do dumb things.
Let's look at each one in turn to see what they really represent.
At the liberal end, you believe all people deserve equal rights, liberties, & basic dignity. All-in on human rights.
At the conservative end, you have hierarchy, autocracy, and subjugation.
You're confusing the liberal-conservative dimension for the left-right dimension.
Sorry to burst your bubble.
It means you think people don't deserve rights & slavery is a fun idea that was poorly executed.
Left-right is about the degree of economic equality & central control of the economy.
Broadly, LEFT = socialist, RIGHT = capitalist.
"Socialist" includes any and all social safety nets -- unemployment insurance, food stamps, housing vouchers -- that are intended to prevent subsistence failure.
Similarly, "capitalist" does NOT necessarily mean laissez-faire radical free market monopolies.
It's a continuum, and every single country on Earth is a mixture of the two.
I've seen this one described many different ways and there is no agreed-upon terminology yet (e.g. "rationalist vs. irrational" is too judgmental for my tastes).
Broadly, intellectualists favor transparency, open debate, empirical rigor, and process.
Ideological space created.
Picture it in your mind, rotate it around, imagine it from different orientations.
If you're into geometry or trigonometry (#nerdlife), you might think of it as a "unit sphere."
A person can be Liberal-Leftist-Intellectualist, for example. (That's me.)
A person can also be Conservative-Rightist-Populist -- that's a Nazi.
I'd characterize Marx himself as Leftist-Intellectualist. On liberal-conservative, he would be neutral (i.e. opposed to hierarchy, but also opposed to personal right to property).
Also, there's that whole killing millions of your own citizens thing, which puts him firmly in illiberal territory.
LIBERALS ARE NEVER COMMUNISTS.
They are literally inherently incompatible ideological positions because pure liberalism has to include enough freedom for personal property and communism inherently does not provide it.
By the same token, liberals can be capitalists.
Again, please stop treating "liberal" as an economic position.
In your own mind, try to position the following:
1) movement conservatives
3) Tea Party
(Keep trying until you can visualize it.)
e.g. Don't agree on left-right? Maybe you agree on good governance.
On the occasion you get more than one aligned, you can pass something big (e.g. Voting Rights Act, Social Security, ACA).
Well, that's how you lose.
If you hold out for a unicorn, you'll most likely get nothing but a donkey with an upside-down ice cream cone on its head.