the difference between American liberalism and American leftism.
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In general, liberalism and leftism are two different axes of a graph. Liberal vs Conservative (also known as Authoritarian) is an axis of how much control over personal lives a party wants to grant the government. A Conservative government would be one that bans things like drug use, prostitution, drinking/smoking, gay marriage/sex, gender transition, abortion, etc. They tend to be more in favor of high police presence, strict penalties for breaking the law, the use of the death penalty, and so forth. Liberals on the flipside would seek to generally allow most personal behaviors. (A wrinkle in this, in America, is gun ownership, which is theoretically an issue that Liberalism would support, but is considered a Conservative issue.)
Left vs Right is about economic policy. Right economics focuses on low government intervention in businesses, low tax rates, minimal regulation, the privatization of services, and so on, under the belief that the free market is efficient and will solve problems best if left alone. Left economics is generally in favor of nationalizing services like utilities and healthcare, providing a broad safety net for unemployment and disability, and tightly regulating businesses in an attempt to minimize abuse. Full blown Leftism involves widespread Socialism or Communism, where private (corporate) ownership of property is abolished and the means and output of production are owned by the people, either directly by the people doing the actual labor or indirectly via national ownership and redistribution.
In the US, the way national politics are set up, the system does not really support more than 2 parties, so pressures have caused these axes to largely collapse. We have Democrats, which are Liberal and Left (at least, ish), and we have Republicans, which are Conservative and Right. In other countries, there are parties that span the spectrum, and you can have Right Liberal or Left Conservative parties, as well as Left/Right + Moderate, Center + Liberal/Conservative, and more specific groups focused exclusively on single issues or positions. The closest thing the US has is the Libertarian party, which claims to be a Liberal-Right party, though tends to focus more on the State vs Federal divide and is perfectly happy allowing states to be more Authoritarian than the Federal government currently allows if it means weakening the Federal government.
In general, either a Democrat or a Republican will interchangeably use Liberal and Left(ist) to describe the Democratic party. On the global scale, though, the Democratic party isn’t particularly Liberal or Left. It supports a few Liberal positions like gay marriage, marijuana decriminalization, and abortion, but on the whole it is pro-police and pro-abolition (the banning of most recreational drug use), and anti sex work. On the economic scale, similarly, they are the more Left option as they support expanding nationalization, but not at a significant rate. The Affordable Care Act was a Center-Right take on healthcare reform, which preserved the for profit health insurance industry, and the best Biden has promised in that regard is an expansion of Medicare to allow it as an alternative to health insurance (and even that is nowhere near materializing). On a Punnet Square (a Left-Right vs Liberal-Authoritarian), both parties fall in the Right-Authoritarian quadrant, with Democrats closer to the middle and Republicans closer to the outer corner.
The only ones likely to use Liberal vs Left distinctly are actual self-identified Leftists, the kind that think Bernie Sanders would have been a step in the right direction but not nearly far enough. They will often dismissively call Democrats “Liberals”, implying that they only care about “identity politics” issues and not actual economic solutions.
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