Crucial difference between this two types of guns: airsoft guns shot plastic BBs and paintball guns shot paintballs. This is THE difference, but we cant forget what is inside of those guns, their mechanisms are totally different also.
Lets start with looking into paintball gun: they use either compressed CO2 or regular compressed air. It’s a quite simple mechanism. But it’s another story with airsoft guns… They use gear boxes, electric motors, batteries… Its look like lots stuff is needed to fire a simple plastic sphere.
Inside of an automatic electric airsoft gun is interesting indeed. A number of gears are turned by small electric motor. This part of mechanism is used to cock back a big plunger/spring, which is used to compress air in a airtight chamber. When compressed air reach a certain pressure, a release valve is opened, this allows air under a big pressure to propel out the plastic BB. This process happens very fast and allows airsoft guns to fire around 15 shots per second.
Also, few more airsoft guns type exists. Most popular and notably is airsoft sniper rifle. Sniper rifles are manually cocked, single shot airsoft guns. They don’t have gears inside. They are not for “trigger easy” people, since you need to manually cock mechanism before every shot, but their advantage is superb accuracy and high velocity of BBs.
Paintball guns function on a similar way, with air thank filed with compressed air or CO2. Most common is CO2, since its more powerful (more pressure on the same cubage). Its also last longer then plain compressed air. Most of paintball guns are semi-automatic, which is disadvantage comparing to fully-automatic airsoft guns. Bot types of guns have a similar problem: paintball guns need to refill their gas thanks, and electric airsoft guns need to change their batter fairly oftern.
In the game, main difference is that paintballs leave visible mark of color on the hit place. On the other hand, BBs don’t leave any mark (beside pain) so player have moral obligation to yell “hit” if he’s shot by another player. Small but very important thing.
Game tactics are pretty much the same, used terrain is similar, urban (towers, bunkers, buildings, etc.) and rural (forest, fields, etc.) Since both types of guns fire their ammunition at the same speed (FPS) they are both safe to play indoors and outdoors.
Conclusion: if you wanna mark your opponents with a large paint mark, and cause them fair amount of pain (if needed equipment is not worn) then you should chose paintball. But, if you wanna get trigger happy and fire more then 15 shots per sec, pouring storm of BBs on your foes, then you should try airsoft. Also, price of paintball ammunition is fairly bigger then plastic BBs. My opinion: try them both, and see what type of ammunition you prefer to fly over your head