They're all pretty much the same, but you may find better/more secure/stronger stitching on the dedicated grappling rash guards, but I've used a couple Under Armour RG's and they seem just as good as my "grappling" rg's.
I think the main difference is the name and logo on the rash guard, IMO
As for your staph, just ALWAYS wash off immediately after you train. Most gyms have showers...don't be shy, jump in and even if you don't use soap, at least rinse off well and then shower with soap when you get home.
You have about 20 minutes after training before your body cools down and your pours close up. You have to wash before you cool down.
If you wash off then you should never have any staph or ringworm problems.
You also MUST wash your Gi, rash guard, fight shorts, jock strap etc as soon as you get home after EVERY class.
It should be common sense, but so many people just don't do it.