New Left: It's not really that new now. The 1960s were a long time ago now. Their main concerns were cultural and social, with environmentalism, anti-war, civil liberties and equality for women and minorities being the main issues. Anti capitalist, but less concerned with economic issues overall.
Regressive Old Left: All things old are new again, and these guys are called "Tankies" now, I understand. Political authoritarianism based on Leninist or Maoist theory. Economically far left to a fault. Culture is not a central concern, but they are repressive towards cultures that are seen as "reactionary" or inhibiting "class consciousness." Which can be just about any kind of culture they can get their hands on.
Old Left: Concerns around organized labor and Marxist, Keynesian or some other kind of center to left wing economic theory. To the extent that they care about social and cultural issues at all, these guys are generally opposed to racial and gender equality, but reject identity politics and tend to see inequality mostly, if not entirely in economic terms.
Regressive Alt-Left: These folks have only just begun to rear their ugly heads. Cultural authoritarianism based on nationalism, racism or anti-feminism. Their anti-feminism and/or anti-Islamism is less motivated by liberal concerns than they'd have you believe, and descend - not always consciously - into the fever swamps of extreme nationalism, racism and sexism. Their economics are autarkic, nationalist and statist. While Donald Trump is probably not one of these, many of his followers are.
Alt-Left: Oppose the influence of white male guilt in postmodern leftism, and are thus not opposed to advocacy on behalf of European culture, people of European descent and/or men's rights. They're weary of political correctness due to concerns surrounding civil liberties, freedom of speech and anti-white/male bias. They worry about mass immigration and the Islamization of European and English speaking countries on liberal grounds: Islam being repressive towards gay and women's rights, mass immigration driving wages down, and so on. Where feminism is criticized, it is for being censorious and misandrist. Most alt-leftists advocate some kind of center left economics, a minority are farther left and more thoroughly socialist.
Regressive vs. Non Regressive: Regressive belief systems tend to be closed, tribalistic and irrational. Non regressive belief systems tend to be open, universalist and rational. Keep in mind that this is a continuum, not a strict either/or thing.
Overlap: Not uncommon, but one almost always dominates, and one of the two overlapping systems is almost always old left, regressive or not. The trajectory of the post WWII world has been from old to new, and in the future, possibly to alt.