A keyboard can mean a synthesiser, an organ, a controller keyboard that does not produce sounds - or any instrument (including piano) that's played using a keyboard.
Not all keyboards are "touch sensitive", which is an essential feature of a piano.
With a touch sensitive keyboard, the volume of a note depend on how hard/fast you press the key. Non touch sensitive keyboards are very limited.
Pianos (and better quality keyboards / electronic pianos) have weighted keys with a very positive "feel", emulating the feel of a traditional mechanical piano key mechanism.
A piano, whether traditional or electronic, is a keyboard instrument with just one sound set.
A decent keyboard synthesiser than can can emulate multiple instruments may well be as good an instrument as a dedicated electronic piano.
eg. The keyboard synth I have can emulate different pianos in addition to many other instruments; the only major differences from the top model dedicated pianos is that it cannot take the full set of piano foot pedals, which high end instruments can, and it does not have fully weighted keys.