Question

A wave and a pendulum are both oscillators. why isn't a pendulum a wave? Please help ..

Answer 1

-- A wave travels from place to place. 
   A pendulum just sits there.

-- A wave carries energy.  A pendulum has energy,
   but doesn't take it anywhere.

-- A wave is a traveling pattern of maximums and minimums
   that all exist at the same time but in different places.
   A pendulum is a stationary pattern of maximums and minimums
   that all exist in the same place but at different times.
   (I made this one up just now;  I really like it.)   

What makes you think that all oscillators must be pendulums,
or must be waves, or must be both, anyway ?

A guitar string is an oscillator that has waves on it,
but no pendulum anywhere nearby.

A car horn is an oscillator that sends waves out
but there's no pendulum anywhere nearby.

An analog wrist watch has an oscillator in it, which is
actually a torsion pendulum, but there are no waves
anywhere nearby.
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Going just one step further with the logic of your question ...
If the logic held water, then we would have to ask:
A horse and a dog are both animals. 
So why isn't a horse a dog ?