Don't fret about the "B". There are ONLY TWO Moen cartridges, the brass one and the plastic one. We recommend the plastic.
If they are selling a cartridge for 12 bucks or so, it may be a generic. We recommend the genuine Moen piece, which is usually $15+. If you think that spending $35 to repair a faucet is anuything other than an incredible bargain, wait 'til you get the bill from the plumber you have to call because you tried to get it out without the $15 tool, and screwed up the body. Add a couple of zeros!!
I used the tool to remove the stem but apparently I didn't remove the entire stem. The part I did extract is brass but it does not look like the replacement. Do I really have to call a plumber to get the rest of it out... or is there another tool?