In the first one he doesn't ever find the bad guys, and neither do the cops. He just sort of shoots over a baited field, if you know what I mean.
In the second one and third ones he goes after the guys who hurt his family, which is more what I think of as vigilante action.
In four he's sort of a one man "clean up LA" committee, and in five he's back to seeking revenge.
I may have some of these wrong, because they do kind of run together, and I didn't see them when they came out. They really take me back to the 70s and the cocaine-driven crime wave that swept over the cities, along with disco. I'm not sure which was worse.