hi Ozmous:

there is( Appoggiatura)

http://upload.wikimedia.org/wi.....iatura.png

The first half of the principal note's duration has the pitch of the grace note (the first two-thirds if the principal note is a dotted note).

and there is ( Acciaccatura)

http://upload.wikimedia.org/wi.....catura.png

The acciaccatura is of very brief duration, as though brushed on the way to the principal note, which receives virtually all of its notated duration. In percussion notation, the acciaccatura symbol is used to denote the flam rudiment, the miniature note still being positioned behind the main note but on the same line or space of the staff. The flam note is usually played just before the natural durational subdivision the main note is played on, with the timing and duration of the main note remaining unchanged.

and what in the pic you post is Acciaccatura.

and you can watch this: