Here's a quick rundown between the different types of intakes. I'm going to use AEM for the examples, but any company would suffice.

Normal: Usually people referring to just the filter.
Pros: Most filters last much longer than stock filters so you don't have to buy replacements.
Cons: Performance gains are minuscule, if any. Often times filters worse than a stock filter.


Short Ram: Replaces the stock rubber piping from the throttle body to the air filter with solid (almost always) metal piping, usually shortens the distance between the two, but not always the case.
Pros: Start seeing measurable power gains.
Cons: Generally not the highest performance. You gain high end horsepower at the expense of low end torque in most applications.


Cold Air: The same as a short ram except this time the piping is longer so that the filter can get air from outside the engine bay (usually from inside the wheel well), hence being called a cold air intake; the air is colder outside the engine bay.
Pros: In general the best performing intake.
Cons: Almost always the most expensive.