The phrase "Keyboards" tends to be a generic term encompassing many types of electronic musical instrument where the common denominator is a piano-style keyboard.
In contrast when we speak of a piano we are generally referring to either an acoustic upright or Concert Grand piano. However, in latter years these too have become electrified with the addition of in-built microphones, microphonic sensors and transducers that allows the amplification of the instrument.
Digital Keyboards & Pianos
Another differentiator is that on the whole "keyboards" suggests an instrument of an appropriate size so that it can to be transported from venue to venue, whereas in general terms a piano usually resides in the same permanent location - be it at a home, studio, a theatre or in a school assembly hall. In fact one of the real advantages to modern keyboards is that they have within them the technology to emulate the sound of a concert grand piano, with the added advantage that they can be transported with relative ease.
Emulating Piano Tones
Contemporary keyboards use sampling technology to record or "sample" the notes of a grand piano, which are then internally stored in the memory and then played back by pressing the notes on the keyboard. In this way manufacturers such as Roland, Yamaha and Korg can produce small footprint keyboards that have completely realistic acoustic instrument sounds stored within them that can be recalled at the push of a button.