I don't think it is different. You can use servo.h for hobby as well as full rotation servos. Hobby servo often go from 0 to 180 degrees whereas the other one goes 360 degrees.
Not quite - a hobby servo moves somewhere in the range of 180 degrees - depends on the internal stop in the geartrain.
A continuous rotation servo givesd you some control over speed. 90 degrees is stop and 0 degrees is full reverse and 180 degrees is full forward. You have no control over positin, just some control over speed with a few degrees around 90 as stop.
A hobby servo can be modified into a continuous rotation servo with a couple resistors and some destructive hacking...