The difference being, these species generally will become extinct rather quickly (relatively speaking) because their genes weaken due to no new DNA being introduced. However, the Amazon Molly has managed to not only survive but become one of the strongest, heartiest fish out there.
The oldest species still alive on this planet reproduce asexually...

There are different strains of the molly because of mutations to the genome add up as time goes on. You don't always have a perfect clone of the female (I could probably look up the probability but I'm tired). Small mutations can cause large phenotypic changes and large mutations can be mostly unexpressed depending upon the location in the genome. Mutations happen at a steady constant speed and is a function of generation interval.
If I wasn't so tired from typing a term paper for my university course I'd do a quick little google scholar search for you on the subject. You just know something like this has been extensively studied and most of the genes involved have been named and perhaps even sequenced.
As to the lack of believe that you have them in you tank. They are either amazons or a very highly inbred molly strain - sibling bred for 10+ generations. However if you have no males from this set of babies, it's probably the amazon.