Liberal in America used to refer to the progressive left, which I understand is already different than most other countries who use Liberal to refer to Classical Liberals (which we generally just call conservatives or fiscal conservatives). However, to make things even more confusing, the term now mostly refers to centrists thanks to the, “Third Way,” Democrats. They were basically a mix of more Neo-Liberal fiscal policies with more progressive social policies; Bill Clinton is the textbook example, supporting gun control and early education while gutting welfare and deregulating Wall Street. This kind of Third Way Democrat basically became the standard of the party, which therefore made them standard of American Liberals. People farther left than these Liberals started referring to themselves as progressives or leftists instead.

So, tl:dr; Liberal used to be a progressive, but now mostly means left-leaning centrist.