Hi there bloodbrother,

A keyboard is the general description. Synths, arrangers, and pianos are all thechnically speaking keyboards (is board of keys).

Piano you know.

Synth is like a piano, but with many different sounds, and other functions depending on the model.

Arranger is an instrument that allows you to control a whole backing band with one hand (auto-accomp), while playing melody with the other (or singing), in one-man-band style.

Because an arranger is a do-it-all, most people who play in bands use synths, because they don't need the auto-accomp.

Hope this helps,

Zalman