The really quick and simple way is that all of the model 15s have a hump*, and the 201-2 has a white light switch integrated into the machine plug. On the 201-2 the lamp is built into the front of the arm, but on other versions of the 201 it is not.
* There are Singer models that share the hump and general appearance of the model 15, but they’re pretty uncommon.

More detailed comparison

The positions of the tensioner and take-up arm are also a quick way to tell them apart, along with the fact that the face plates are contoured differently.

View from the back

It was pointed out to me that the back of machine is often displayed by sellers that don’t know any better, so here you can compare the two machines from behind. You can still see the tensioner and the hump in the arm of the model 15-91. The 201-2 has no light on the back, but the light on the 15-91 may be missing, so “no light on the back”, isn’t necessarily proof positive that it’s a 201-2.

The Singer models 15 and 201 in all of their different versions are both really good machines. The 201 was, and remains the more expensive of the two models. The price of the model 15 tends to be artificially depressed since it sold so well and has lasted so long that they are still quite common, at least in the United States.