for us non-americans, can someone please explain what general political aims the 'moderate' and 'progressive' parties represent? And where are they on the republican democrat spectrum?
The "progressives" generally want to limit gentrification, prevent renters from being evicted, and add more subsidized housing. The "moderates" generally want to make it easier to build more housing of any type. You could broadly characterize the two groups as "default skeptical" vs. "default supportive" of real estate developers.
But housing is only one point of disagreement (albeit one of the most significant), plenty of people have more nuanced positions than this, and these camps are not entirely uniform across issues. Other points of recent disagreement include Covid lockdowns, what the school board should focus on, how hard prosecutors should go after police misconduct vs. minor crime, responses to the homeless, how much power the board of supervisors should have vs. the mayor's office, ...