That's an escheveria and it looks like it has some baby offshoots. It will spread into a nice mat if you plant it in a bigger pot or in the ground. It has nowhere to grow in that pot, so it's reaching out. It's very healthy, just needs more space. All the rosettes should be sitting flat on the soil.

Keep in mind that very few succulents actually like full sun in the desert. They sunburn and die back.

They grow well in the shade of trees and patio overhangs and north sides of houses.

When you water them, SOAK them thoroughly and then let them dry out almost completely. You can kill them with frequent, light waterings.

That's Aeonium arboretum... Probably 'zwartkop' or atropurpureum. Will grow quite large in ideal conditions. You need a soil that drains more freely, then you can give it some deep waterings.. Morning sun, bright afternoon indirect light.

-Ming