All these terms refer to the little 10 hole diatonic harmonica. There are many styles, brand names, models, special tunings, and keys available. Many of the lower cost harmonicas are good values. The heel of your right thumb rests and pivots on the length of your left thumb and raps around under the harmonica forming a sound chamber, left fingers lay along the length of the harmonica, the right fingers form a cup, meeting or slightly overlapping the left finger tips.
Open hands give a brighter, louder sound.
Closed hands give a mellower, richer sound. The hand position can infinately vary the sound of the harmonica. Hand position is not he only thing that can change the sound or tone of your harmonica. Playing a single note comes with great difficulty for some. Relax, you may be trying too hard.