These are the criteria for evaluating any variety:
Self pollinating: anthers are close to the stigma meaning pollination can happen without assistance. However, manual pollination can still help fruit set/fruit size.
Self fertile: it can set fruit using its own pollen
Self sterile: it requires pollen from another variety to set fruit.
also,
Universal pollinator: a variety with pollen that can pollinate most other varieties.
American Beauty is for sure self fertile and is also a great universal pollinator. However there may be two different cultivars that are known as American Beauty- my flowers have long stigmas, for example, and are not likely to self pollinate. I've seen other "American Beauty" flowers that have short stigmas.
I also have Halley's Comet and Delight. They are both self sterile. Also, Halley's Comet cannot pollinate Delight, nor can Delight pollinate Halley's Comet- they are genetically too close. However, American Beauty can pollinate both of them.
Growing a variety like American Beauty and/or Sugar Dragon/S8 can really make things easier. If can be difficult if you have too many varieties that require cross pollination... it is terrible to see a self-sterile variety light up with blooms if you don't have any pollen frozen and your universal pollinator won't bloom in time.
Also, it goes w/o saying but "self pollinating" is only a relevant characteristic if the variety is also self sterile. It won't matter if the anthers can get the pollen to the stigma w/o assistance if the pollen is useless.