I can start and you can finish/correct me where im wrong.
Air to Air
Consists of an heat exchanger that allows the outer air to rush past and cool the air being forced through the intercooler and into the engine.
The cost of air to air is relatively low compared to other cooling methods. It is also a very reliable form of intercooling. You dont have any pumps or reservoirs to purchase or install.
Can only cool the air as much as the outside air provides. The longer intake piping and all the additional curves that run the air to and from the intercooler result in drop in psi thus loosing potential hp.
Liquid to air
Another form of intercooling that consists of air passing through an intercooler with a liquid medium that draws away the heat from the intake air. Consists of a radiator, water lines, a water pump to circulate the water(or other liquid), a reservoir to hold the liquid, and a liquid to air intercooler.
Much more efficient at dropping the intake temps. Can drop the intake temps further than just air to air intercooling. Less drop in psi in the intake piping b/c the piping doesnt need to be routed to the front bumper and through the intercooler. Typically the intercooler can be placed inline so that the most direct path can be used. For additional cooling, ice can be added to the reservoir and can help drop the temps even greater.
Price. More components to buy and the straight through (barrel type) intercoolers are pricey. Also it is more complicated and if the pump goes out, you get little to no circulation of the water resulting in no cooling.
I think thats a good start! I hope everyone can add a little information.
Also could you add a section on the different MAF styles? Im not even sure what the difference between the two are. If its just location or if you need a different maf etc. Thanks orange!