When a star begins to die, it uses up its last energy so quickly that it swells up, and then explodes.
Most medium mass stars such as our Sun DO become red giants. Smaller stars do not have enough mass to initiate helium fusion when the hydrogen supply begins to run low, and do not become red giants.
Typical red giants are red giants for about a couple of million years.
Yes red giants are the largest. But the bigger stars of red giants can be called red hyper giants.
Aldebaran