Bots are automated programs reading the site. A number of companies run them, and the board knows about 50 of them. They don't login like real people do, but the board identifies them in other ways.
Adsense is a program run by Google to show relevant adverts on the pages. You can read about it
here. The Adsense bot reads the pages to tell Google what kind of adverts to display. That one is allowed to read the registered user forums. It doesn't give any information to Google Search.
I believe Yahoo Bot indexes pages for Yahoo Search.