Theme Manager icons + mutiple themes

Q1: I did a search to find out the difference between the two icons below and found a post or two but the question went unanswered, so… could someone tell me the difference between these two icons and when one would use one over the other?

Q2: While I’m here, is there a way to save themes so you can switch between them to let the client decide? I guess this may have something to do with the Bootstrap custom settings? Thanks