Tiffany, very nice! I used to have both
Angel Wing Begonia (Begonia 'Sinbad') and
Beefsteak Begonia (Begonia 'Erythrophylla'). Seeing your Begonia Beefsteak reminded me to upload an old photo of mine to the database.
Janet, nice ones you have there too!! I don't know Begonia's all that well but your first one reminds me of one I grew a number of years back that was named
Angel Wing Begonia (Begonia 'Lois Burke')
I've grown a few Rex types over the years too but they never seemed to do well unless I kept them in a terrarium. The Rexes have such gorgeous leaves!