Training / Workout Shoes?

Hi FB Family!

I've noticed that there are workout videos where Kelli or/and Daniel don't wear shoes, though they are usually only strength/ light cardio/flexibility workouts.

I use my running shoes for doing workouts, would that be okay? They support my feet a lot since I need shoes specifically designed for stability. (when running) But I also sometimes don't wear shoes, usually when I do core training because shoes add weight to the feet and makes the core training a bit harder.

Are there shoes specifically made for training / working out? If so, what do you recommend?

and I'm curious: What do you guys use for shoes? Or you do wear shoes at all?

Do shoes even matter when working out? hehe

Sorry for a lot of questions. Let's discuss this out though, since no one has started the discussion yet. I personally think shoes do matter, because my mom had earned a foot injury because apparently she was using the wrong shoes for running (she is flat footed and needed specific shoes for running) What if something similar could happen during working out?

I hope this discussion would help prevent this and help other people having similar problems with shoes :)