can someone please explain the different ammunition types?
I have no clue what people mean by +P and hydrashok
Certainly. For small arms (revolvers, pistols, rifles, etc.), there are essentially two major types of ammunition available and in common use, and numerous other types which are far less common. I'll go over the two major types first
First of all, the most basic type of ammunition, which the military is required by the rules of war to use, that being ball ammunition (also known as full metal jacket, or FMJ, or copper jacketed). Essentially, it's probably what you think of when you think bullet. It's going to be one solid piece projectile.
The second major type are expandable rounds. There are slightly different types (jacketed hollow-point, softpoint, etc.) they're all designed to do essentially the same thing, have the bullet expand into a mushroom style shape upon initial penetration. A bullet which expands has a larger cross-section, which does more damage. Hydra-Shocks are simply a well-regarded name brand of hollowpoint ammunition, made by the company "Federal."
As for the other types of rounds (which have their devotees, but represent a tiny fraction of sales), the biggies would probably be frangible (bullets designed to shatter into tiny shards on impact), flachette rounds (think a steel dart shot from a gun), non-lethal rounds (think plastic/rubber bullets, bean bag ammunition and such).
The term +P is a technical term, which refers to a high velocity loading of a particular cartridge. Essentially, a particular round has a set specification for the amount and type of powder loading it's supposed to get, and a spec for the amount of pressure the round generates when fired. A +P round indicates one which has been "juiced up" to a higher than specification loading factor. It's a marketing term, kinda like how you can have a V8 engine with a Turbocharger. Think of a +P loading as a hot rodded bullet.
Here's a wonderful site which will give you tons of information from someone incredibly much more versed about the subject of ballistics than anyone here, it's worth a look. It has some good photos and charts as well.
The mechanics of terminal ballistics