Definitions and commonly used terms:
1) traditional piano sound,
2) filtered pianos with some effects,
3) CP80 - sounds like a toy piano,
4) Rhodes piano - sounds like a hybrid between a piano and a guitar,
Pad - used to create a texture, a background sound. It’s more felt than heard. There’s different ways to play a pad, namely bright/loud or dark/subtle. As a keyboardist you want to help create that space, the width to the sound. The mix will sound a lot wider with a pad in it.
Synth - a harsher sound, and a more melodic sound. Typically used to play a repeating phrase or arpeggio. You can filter the synth like a pad to create a darker tone etc.