Remember it's not actually "bbPress", it's an entirely different program, actually a very large plugin that runs under WordPress. They kept the name and mashed up the support website with both programs for some reason that cannot be comprehended, and will keep people confused for a few years to come.

I cannot stress this enough - if you are crazy enough to abandon the standalone version, be sure to backup EVERYTHING before you change to this wordpress plugin. Not just the database but also all the core and plugins etc. - you will definitely regret not doing so afterwards.

None of my plugins will work with the bbpress "2.0" version (and never will for what it's worth).

Also if you understand technical issues, imagine a single database table that holds not just every wordpress post but every topic and post from the forum side and the technical issues this causes with mysql locking tables for certain operations (writes, etc.) Large sites should take heed at that core concept.

So in a nutshell:

bbPress 0.7-0.9 standalone - standalone, super-fast and fixes some important legacy core problem that wordpress had as Matt gets a chance at a "do-over"

bbPress 1.0-1.1 standalone - Matt changes his mind on a whim and decides to have them rip out the WordPress core to make backPress which will then power bbPress by ripping out the core functions in bbPress - but it adds an extra layer of "communications" between the two so bbPress 1.x is 50% slower than 0.9

(Sam Bauers leaves Automattic/bbPress at this point, so bbPress is in trouble)

Then Matt changes his mind again on a whim and decides WordPress core will never change and never be standalone so backPress is essentially dead in the water despite all the effort put into it, and converting bbPress to use it

bbPress 2.0 - a WordPress plugin written from scratch but keeping the same name as the standalone version, essentially so buddyPress can have forums without having to use the standalone version, regardless of the massive performance hit