Joe Biden is not a "moderate" Democrat. He's always been among the more progressive members of that party. These days, however, he is flanked on the left by a growing group of radicals who refer to themselves as "progressives." Representatives Tlaib, Bush, Bowman and Ocasio-Cortez are all members of the Democratic Socialist Party of America. That party's platform calls for central planning of the entire US economy, which, if history is any guide, would make every American a lot poorer, and less free. It is not progressivism as defined by scholars or politicians such as John Dewey, John R. Commons, and Robert LaFollette. Nor is it Joe Biden's progressivism or Barack Obama's progressivism or Hillary Clinton's progressivism. It is equally a mistake to refer to those politicians and scholars as "moderate" Democrats, a term that better describes Bill Clinton and his "New Democrats" (similar to Tony Blair and the "New Labourites" in the UK.
While the precise terms we use to define parts of the political spectrum are not so important, it is very important to use the terms consistently to avoid conflating different parts of the spectrum. These days, it is convenient for politicians on the left to accuse every one to their rights as "conservatives," and for conservative politicians to refer to everyone to their left as "socialists." That kind of labelling always sheds more heat than light. Reality is always more complicated than labels. But if we are going to use labels, let's at least be consistent about their application so as to highlight meaningful differences between political positions.