That's right. From what I can tell, alicorns are an equal mix of each of the three types of ponies. Celestia's particularly tall, but Luna and Cadance are closer to my height.

I don't think there's anything different besides those... well, Celestia can raise and lower the sun, and Luna the moon, but I don't know if that's because they're alicorns, or because of some other reason.