Daisy Fleabane isn't an aster, but it's in the larger aster family. A casual glance could easily mistake it for an aster. The flower of a Rush Aster is white or pale blue. It's endangered in Pennsylvania, so they're encountered infrequently. One of my field guides lists 75 asters in the northern US and Canada, and there are a lot of white asters. Listing the specific differences between the species that you asked about wouldn't guarantee that you could identify the asters that you encounter. Check the references below for more specific information.
When I photograph wildflowers, I typically focus on close-ups of the flower and don't include enough of the other characteristics to positively identify the specific species. In many cases I could not tell you the species from the cropped photos that I post.
Asters can be tricky to identify. Many of the white asters have similar characteristics, and some have considerable variability between plants. I'd recommend "A Peterson Field Guide to Wildflowers: Northeastern and North-central North America" as a good first guide for wildflowers in the northeastern US. My copy is probably forty years old, and I still refer to it regularly. A word of caution about printed field guides: they soon become outdated. The asters, in particular, were recently reorganized with some species combined and the family divided into separate genera. Since individual plants can have half a dozen common names, you might find the plant in the field guide listed under a different scientific and a different common name from source to source. The USDA website is a good place to sort out the confusion between scientific names.
https://plants.usda.gov/about_plants.html
Searching for "Aster vimineus" there led me to the page for Symphyotrichum lateriflorum, the current scientific name. You can trace the historical names by clicking the Synonyms tab. That's actually the page for Calico Aster, which Peterson calls Aster lateriflorum. The latest reorganization combined Small White and Calico Asters, so they're now considered the same species.
I've had good luck with the following websites. They're kept up to date on name changes, and most of the flowers that I search for can be found there.
