Most 'white' horses people see are grays,
However there are also cremellos and perlinos that get confused for whites.
But there are white horses, they are generally an extreme expression of pinto pattern, genetically they could be any color, but white may be all you can see. In my opinion I would call that a white, if I owned one and was asked the color I'd say white. Now if I was planning to breed it (or standing at stud) I would need to know the genetics behind it, and probably wouldn't call it 'just white'. I don't really think they are that rare, I can think of three here locally. White pony mare down the road w/ blue eyes, had a white foal w/ brown eyes. Another guy in town has a little blue eyed white mare. That's three I can think of in this little town.
The most obvious way to tell the difference is their skin, gray's have dark skin, cremellos/perlinos have pinkish skin, but it's a creamier color of pink (hard to explain) skin and their eyes tend to be a very pale blue. White horses have very pink skin and may have blue or brown eyes, typically the blue eyes are brighter then a cremellos. I'd say the biggest health issue would be sun burn, I've heard people say their bodies can burn, but their faces are all I've had experience w/ them burning, and that's any white faced horse. And if they have pink around their eyes they can be more prone to skin cancer there.