Easy this one:
Cotton - the inner is made from cotton, although often having a mesh backhand.
Half Chamois - the palm is made from chamois, while the backhand is mesh
Full Chamois - the entire inner is made from chamois
Chamois is more absorbant than cotton so is often a better choice. You can get all of the above in both padded and unpadded - personal preference. I know there are keepers on here who prefer the feel of an unpadded inner but as I keep to lads who regularly bowl in excess of 75mph I prefer the padded option. Sometimes i wear 2 inners on my dominant hand if the pitches are really quick.