I've seen lots of explanations of the mil spec vs commercial buffer tube dimensions. Do the threads on the lower fit both, or do they also come in mil spec and commercial dimensions?

Threads are identical in size although they are produced differently.

What WW1 said.

The threads are a different cut and and the tube diameter that the stock slides over are slightly different (commercial slightly larger diameter)  so the stocks are different.

Both work and will thread just fine into the receiver.  Just be sure to use the correct stock inside diameter, mil spec or commercial, to match whatever the tube is.

Correct mil spec tubes have slightly thicker walls under the cut  threads so should be stronger.  

I have and use both.  My RRA lowers have commercial tubes but whenever I replace anything I use milspec, mostly.  If you switch from commercial to milspec you have to change the stocks as well and that is money.   Both work.

Now, what I don't understand, is why there ever was a difference in the first place.

I want to know the answer to this too, seem like a real waste of time and money.

As said both with thread into the lower just fine, used the same castle nuts, only the tube where the stock fits is a larger diameter on the commercial tubes, also thier is a slight slant on the rear of the tube, probably the easiest way to tell which is which. There are more stock options for milspec vs commercial they can generally be had cheaper.