KraphtBier did a great job with the wheat beer side of the issue.
A kellerbier is just an unfiltered lager that's served at "cold basement" temperatures and has lower levels of CO2 than most lagers. There's TONS of different variations on it but the version that most style definitions focus on are essentially unfiltered helles or unfiltered pils served with lower CO2 levels at higher temps. You'll also see it's close cousin "Zwickel/ Zoigl" sometimes. (I've only found it in Vienna, Austria despite spending plenty of time in Germany seeking it out.) Most of the style guidelines argue that Zwickel / Ziogl is hoppier and this definitely agrees with my experience; what the difference is between a keller pils and a Zwickel then, I have no idea except Zwickel can maybe go a little higher on the SRM scale. -In reality any attempt at broad generalizations often ignores very real examples that already exist.
In Germany you may see "keller" versions of any other German style which basically means that it's an unfiltered version. -Much like the German tradition often adds/ added "bock" to a beer style name to denote that it's stronger than normal. "Keller" means "kellerified" aka "unfiltered". -This is also why Sierra Nevada's "Kellerweiss" name makes no sense at all because hefeweizens, except for "krystalweizens" are already all unfiltered... What are you supposed to do, take it out of the fridge for 90 minutes and pour it into a glass and let it set for 10 minutes so it's slightly warmer and flatter than normal?!?
*Sigh Beer Imperialism marches on..
The yeast remaining in suspension raises the perceived (and actual) bitterness levels as some of the isomerized alpha acids stick to the outside of the yeast cells and will get carried out of the beer when the yeast flocculate, decreasing the bitterness; you have this enhanced bitterness (and extra B vitamins!) while the yeast remain in suspension. I had a bottle Monschof Kellerbier that was in the bottle long enough for the yeast to flocculate and it was an incredible experience; long, bottle conditioning with yeast present is just not a lager experience you get much any more; I prefer kellerbiers even when the yeast has finally given up and flocculated over the typical filtered versions.
P.S. The German beer tradition doesn't add finings; they're not permitted per the Rheinheitsgebot so kellerbier is really about the lack of filtration and the use of a low flocculating yeast; finings don't play a part because it's a German style, not because it's something specific to kellerbier.