The differences between an airsoft and a bb
There are several crucial differences between an airsoft gun and a traditional bbgun. An airsoft gun is a more modern invention that uses the same firing mechanism as a bbgun, but shoots large plastic pellets at lower velocities. This makes them safer for use, especially by kids, than metal BB airguns.
The appearance and feel of an airsoft gun often mimics that of a genuine bullet-firing weapon; whereas a traditional bbgun is often very obviously not 'real.' Because of this, many firearms enthusiasts like to use airsoft airguns for target practice, team war games (think paintball), and collecting. In Japan, where you cannot own a handgun in most cases, sales of these replicas are sky high.
An airsoft versus a bb
There are relative merits to both kinds of airguns – the airsoft gun as well as the bbgun. The former is mostly used for collecting and participation in weekend war games, while the latter is often used for small game hunting, plinking, and target shooting. These two generalizations are by no means set in stone, of course, and it's not unusual to find owners of either using their airgun for any one of those pursuits. The exception being hunting, which cannot be done with the slower, plastic ammo guns.
An airsoft gun might be a better idea for a beginner or a younger shooter because it tends to be much safer than a bbgun. Because plastic pellets rarely pierce skin, while metal BBs can do it fairly easily at close range, the former is a better choice until the user becomes proficient and practices gun safety at all times.