You've used Underwood as an example, but similar situations can be found in other manufacturers' serial numbers within the Database too. 

The problem is that we don't have a definitive list of model names for every manufacturer. Typewriter collectors have had to work backwards using a variety of sources to create lists of the various models that the manufacturers produced. In some cases the names are internal model identifiers gleaned from manufacturer documentation. In other cases the name is simply taken from the badging used on the typewriter, what it was referred to in advertising, or from period reference books. The worst case, and something I'm opposed to, is when collectors arbitrarily create model names. 

To answer your first question, many typewriters manufactured as part of a series of machines look similar. There is typically a base model, which is given one name, and then feature variants of that model, each with their own names too. Two machines may look identical, but because one might have touch control (for example) and the other doesn't, they are in fact two different models.

In the case of Underwood standards from the two decades you mentioned, I've been working on my own list of models based on the documentation that I've come across and the machines I own, and it doesn't completely jive with the Database. Some of the identifying names differ, but the models are likely the same: 
Underwood Model 6
Underwood Master
Underwood Master S
Underwood Rhythm Touch
Underwood Rhythm Touch Deluxe
Underwood  SX150
Underwood Touchmaster I
Underwood Touchmaster II
etc.

With respect to the Database, Ted, its owner, has done a phenomenal job compiling all the loose bits of information that are brought to him by collectors. The Database is a work in progress, and I think its accuracy is steadily improving; however, the trick is to remember that it's a best-guess reference by contemporary enthusiasts, and not a tablet chiseled in stone by the companies that used to make these machines. Some of the data is rock solid, some of it hazy, but it gives collectors a starting point when discussing the history of makes and models. 
 

It does happen that people create personal galleries that contain mistakes, whether it be the wrong model or manufacture year. Ted, and those who frequent the Database, catch most of them, but sometimes there are a few that fall between the cracks.

Not sure what the mystery is. Underwood standards are a fairly well-known entity. Perhaps if you were to reference the specific entries (and by entries I'm assuming you're talking about those aforementioned galleries), then we could have a look and see what you're wondering about.

I continue to be puzzled by the Underwoods of this period as well. For instance, I really do not know what the difference is between the S and SS, unless it's a change to molded plastic keytops. But both are essentially the same as far as I can tell -- carriage shift design.

The Rhythm Touch as I understand it was a change in design to a segment shift machine. The longer line spacing lever came at the same time, but wasn't connected to the shift mechanism change.

With the SX models came, I think, a change to a different spool design and ribbon reversing mechanism -- gone are the universal spools and the grommets on the ribbon, and in its place is basically the Remington mechanism, though on some of the later machines there were special spools (unlike for the "spool-less" classic Remington design). I have what I believe is an SX-150 and the spool compartment has a notation to use the "150" spools, whatever they are -- I find that the spoolless Remington ribbon works fine. The new ribbon reverse mechanism carried forward to the later Touchmaster machines.