It is an Aloe but a different species or hybrid. Someone else might be able to tell you which Aloe it is. Probably you can take care of it as if it is an Aloe vera. I doubt it has any unusual needs.

Get rid of the moss first of all. Your plant is a Sempervivium, and probably lost its roots to rot from growing in such an unsuitable medium. Succulents need well draining soil with little organic material. Florists tend to know cut flowers, not plants, in my opinion, but they will not admit that. Get some cactus and succulent soil and some perlite, and mix them in a 1:1 ratio. Fill a small pot to the rim, and set your rootless plant on top. Then leave it alone for a few weeks in a bright spot. Do not pick it up to check for roots, that will damage them. When the plant seems stable in the pot, you can start watering it. Give it a good drink and then leave it until it is completely dry before you do so again. Do not spray it, succulents generally don't like wet rosettes. Alaso, Sempervivums generally don't do well indoors long term, this plant would be happier outside year round. These are very hardy plants and can tolerate winters in in Zone 3 or lower. happy growing! Breton

It looks like Kalanchoe rotundifolia to me...Definitely a Kalanchoe, at least.

you might want to try the cactus and succulent forum ...