I am very botanically challenged... I have been keeping these alive by bringing them in every year under ultraviolet lights. We have had them long enough we don't know what they are. I believe they are related but not quite the same. What are they? Can I put one or either in the ground next summer and have them come back year after year? I am finally getting old enough to want a nicer yard. I combined and numbered the pictures.
Looks like Portulaca. Coincidentally enough, I was just talking with my mom (born in Paris, Illinois) about her portulaca! She has had it in her flower beds for 40 years, and said that each summer up come at least a few plants. Not perennials per se, but do reseed themselves. I'd say go ahead and put 'em outside next year. Welcome to the Forum!