If its a comprehensive putting thread you want BroD then lets try.
I'm going to say there are definitively two kinds of putt. Push dominant and spin dominant. While everyone uses both spin and push to putt what distinguishes them is how much push or how much spin.
Lets use some rough percentages with pro's for examples (not matter of facts)
Nate Doss - 70% Spin 30% Push
Dave Feldberg - 30% Spin 70% Push
Ken Climo - 85% Push 15% Spin
Ron Russel - 90% Spin 10% Push
Now some may be thinking "Well what about Straddle Putting or Jump Putting!?". The answer is this. There a bunch of stances and ways to generate power for either a push or a spin and the different "kinds" of putts still fall into the push or spin categories. EX: Most straddle putters are push dominant putters but that have more elements of a spin putt in them than say someone like Climo. And in some cases like Markus Kalestrom you have straddle putters who are clearly spin putting. So that means that the "straddle putt" is really more just a stance that most often lends itself to push dominant elements but can really be used for either and doesn't merit its own style. Within these two styles there are all kinds of diff stances and ways to generate power but they still remain either a push or spin style. The only other primary categories you could establish are an anhyzer putt or a hyzer putt (or stable if you want, why not). With these though it becomes more of a line choice as opposed to style. Thus they are not outside of push/spin but supplements to.
Nate Doss - Anhyzer putter
Nikko Locastro - Hyzer putter
Climo - Hyzer
Kalestrom - stable/neautral
but it just becomes a matter of saying Nikko Locastro is a Push dominant putter that uses a hyzer line and a staggered straddle stance. Who generates most of his power from his arm frist followed by his back and then his legs. The "swing putt" I believe it gets called isn't really its own style as much as a set of conditions that I just named. The only thing that could really define it is that the disc is most often released much lower to the ground than other players and some have complained that it can be complicated by derbies, tall grass, and elevation changes...
its late, thats all for now...