Yes, Aristaloe (formerly Aloe) aristata. The reason the baby plant looks different is that it needs much more light. Ideally it should "see" the sun for hours each day through the window if it's going to be an indoor plant. You cannot provide too much light indoors. Right by your sunniest south-facing window would be ideal. I'm not sure what exactly is going on with the mother plant... could just be a bit of the winter doldrums, maybe. Are any of the leaves soft? Are the roots still anchoring it firmly in the soil?
In the spring you should consider moving it (and especially the baby) into slightly larger pots (wider than deep, with holes at the bottom). This plant is a bit sensitive to excess moisture, so be careful to use fast draining soil (say 50% perlite, pumice, or equivalent) and avoid watering when the soil is already wet. Try to let it dry out most or all of the way each time you water, but there is no particular benefit to leaving the soil dry for any extended period. Be gentle with the roots when you do repot (don't break up the root ball) and do not water for about a week afterwards.
More about aloes here.
The Aloes Database