This is the second one. I’ve tried researching what it could be, but I haven’t been able to find it. It looks really really similar to Crassula schmidtii, but the flowers are white and it seems smaller than the pictures I’ve seen of schmidtii, with thinner and more delicate branching on the flower stems.
You were on the right track with the crassula family, but I think it’s a Crassula Exilis (and a beautiful one at that! look at those flowers!)