Look to be some kind of Hiemalis (rieger) type begonias. Smaller one may be tuberous.

A lot of folks consider Hiemalis annuals and toss them after they start declining. You can research how to keep these though as I'm confident that they can be kept for a few seasons.

riegers are considered to be indoor begonias - they like a narrow range of temps that are perfect for indoors. 65F night -72Fday. at most 75F. higher then that and they start declining. indoors east or west window with sev hours of morning or late afternoon sun is best.
they do not like to be pot bound. if they filled their pots you need to xfer them to slightly larger pot: e.g. from 6" to 8".
african violet soil cut with 30-40 % perlite is good. they take a lot of water when growing - do not let them dry up. they like to be moist. may be dry to 1-2" from the top only. and the just water a little to moisten the surface area that went dry. soaking thru every time is not good. they might rot.
i posted sev times about reblooming them (which i did) - search for rieger.