Andrew is right that there is a different style that is a product of the environment and conditions they are fighting in. This is regardless of what their backround is (Muay Thai, Amer Boxing, Grappling, etc.).
Their hands are up differently then people of other fighting sports first off, because they have to guard against strikes up top as well as the shoot and grappling.
They have to transfer their weight for their stand up punches differently also, because they have to center their weight lower then a muay thai fighter or boxer because of grappling.
Their isn't as much wrist twisting when the punch is thrown (for most fighters) as in boxing or other stand up sports because it is too telegraphic when one has to center his weight differently.
And last but most important: They need to be able to transfer energy differently to get power in their strikes from "odd" positions; like from the sprawl, or mount, of guard, or when someone is pinned against a cage wall, etc. This is far different then stand up striking sports as well.
Someone mentioned "dirty boxing." We have a bare-knuckle fighting program that is a staple of what we do (called "Modern Bare Knuckle Fighting). The striking is very similar. When you train how to punch effectively, it is very easy to see the differences between punching styles in combat sports, and why they develop the way that they do.
Paul