Okay, I learned a lot today.
One, I learned that faucet parts are non-standard and vary by manufacturer.
Two, conversion between faucet types, as in single-handle twisty knob like in the picture that I am (un)fortunate enough to have in my bath, cannot be easily swapped out for anything other than a single-handle twisty knob.
Then I found out that two major hardware stores did not carry the valve cartridge (stem) for my particular faucet.
Lastly, there can be many different stem types available, and without knowing the correct type, I might as well not bother.
Why did I learn all these things? The faucet in my shower is kinda whacky and would not maintain a constant water mix resulting in cold or scalding water coming out of the shower sporadically and when you least expect it.
Continuing to play plumber, I cleaned out the partially plugged up aerator on the kitchen faucet.
Also installed the new battery I bought for the Roomba on eBay and set it to charge for a while.
Almost washed the car(s) but instead spent the evening watching series on hulu.