That "moderate left", Democratic socialism, is not left at all, but a centrist position. The world is so right heavy that people think that maintaining a softer version of capitalism is "left". It takes advantage of the emotional value of the word socialism, but never seeks to end capitalism.

The left is strictly anti-capitalist. Full stop. That includes MLs (maoists, dengists, Stalinists, and orthodox maxist-leninists and some smaller variants) and anarchists. One of those groups is very clear about what socialism is and the other isn't socialist at all. Both believe in an end goal of communism with radically different ideas of how it can be achieved.