Good definitions of political terms:
https://crookedtimber.org/2018/03/21/liberals-against-progressives/#comment-729324
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On definitions: here’s a set I find helpful, although certainly incomplete.

“Liberals” are focused on equality of rights among people. What count as rights is heavily contested, but in general universal rights are the liberal focus. Liberals are opposed to privilege (private law-where class/status are legally important) and fairly are criticized for “the law, in it’s magnificent equality, forbids both rich and poor from begging for bread and sleeping under bridges.”

“Leftists/socialists” are focused on economic inequalities, generally influenced by Marx to some degree. Leftists are opposed to economic inequality, and often see it as a cause of social/rights-based inequalities rather than seeing those as separate things. Leftists are opposed to difference-making inequalities in private property, and are fairly criticized for “Wonderful theory, wrong species.”

“Progressives” are focused on social/identity-based inequalities, often based on feminist and critical race theorist social critiques. Progressives see economic inequality as entangled with social inequality, but see social inequality as the more immediate concern. Progressives tend to focus on the social and institutional factors that maintain social inequalities, and to be very focused on ensuring that all institutions serve the needs of society. Leftists criticize progressives for focusing on the wrong problem; liberals criticize them for re-inventing privilege.
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