blue-green trailing succulent

Repotted this little plant which is a favorite, though I still don't know the name. I just wore my eyes out online looking and looking- it's not donkey tail, or string of pearls, or sedum sieboldii, though similar to all of those. Well. It has outgrown its pot:

There were little baby plants in there, but I knocked most of them off accidentally- 

A lot of leaves fell too. I would worry- but in trying to find its name also read more about the care of trailing succulents in general. The leaves are fragile. They damage easily.

New pot:

My inclination when repotting plants is to water them thoroughly afterwards, but I read the instructions on the bag of catus potting mix this time- and it says to put the plant out of direct light and not water it for a week or two. So I did.

I stuck some of the dropped leaves into another pot, just to see if they'll grow. Although I think they're supposed to sit and dry out first? Well, if these do nothing, I'm sure a few more will drop.

Next to the spider plant.