There are two main types of harmonicas (sometimes called "harps"), the chromatic harmonica and diatonic harmonica. Although the chromatic is extremely versatile, the harmonica which is mostly used in blues, rock, country and folk is called the diatonic harmonica ("blues-harp").
The chromatic harmonica is mostly used for jazz, classical, and pop music.
It has a button on the side which allows you to play the normal major scale, and with the button depressed, gives you all the half steps or notes in between.
This allows you to play any scale, in any key, but you can't bend notes very well on this instrument so you don't get the same "bluesy" sound as on the diatonic. The chromatic harmonica hole layout is similar to the diatonic hole layout, but not the same, so song tablature is different.
Some chromatic harmonica- players are Stevie Wonder, Toots Thielemans, and Larry Adler.
The diatonic doesn't have easy access to all the possible notes like the chromatic harmonica but many of the notes that are not naturally found can be acquired by "bending" certain draw (inhale) and blow (exhale) notes. It is the "bending" sound of the diatonic that attracts most people to it. Some diatonic harmonica-players are Bob Dylan, Neil Young, James Cotton, Sonny Boy Williamson, Mick Jagger, Little Walter, Paul Butterfield, Mickey Raphael, John Popper, Charlie Musselwhite, Huey Lewis, Jimmy Reed, Sonny Terry, Steven Tyler, and so on.