In a nutshell there are generally few different types.
One type is mechanical. Always linked to the cabinet via some sort of mount. Targeting is accomplished via some form of pot or grey encoder to determine what position the gun is held at. If anything these are most similar to how fixed steering wheels or analog pedals work. They are not like mice.
Another type has an optical eye in the muzzle and is tightly integrated with the CRT commonly used. In short these types of guns are non functilning with any modern flat panel screen. Consoles typically use that technology.
Another type uses similar technology as the Wii in that the sensor in the muzzle is far more sophisticated but does require additional "sensors" around the monitor to get a "fix". This is the preferred method as it is a fair compromise on cost.
I haven't seen too many of the final design but it leverages a camera on the cab and some sort of tracker in the gun. Think 360 or PS3. It is the opposite of the Wii method and more importantly, it moves the bulk of the processing to the computer inside the box.
There are a few other, lesser, designs but you are unlikely to come across them. Nearly any gun can be retrofitted from one type to another. Thing is it helps to know what type hou have and what type you want to switch to as that will indicste what options you'll excercise.
If the trigger is sticky or problematic but the gun works fine otherwise I would diagnose and fix that problem first. Changing gun technologies is, IMHO, a hassle and I've got more than my share of unfinished gun mods on my work bench.
Transplanting guts also works but, it too, is a lot of work if you don't choose a good gun housing for it.