Do sustain pedal and damper pedal refer to two different things ?

The damper pedal on my PA-80 holds the note forever after I take my finger off the key. My old PSR 510's sustain pedal holds the note and makes it fade away slowly, rather than holds it forever. I prefer this behavior way better than holding the note forever which I almost never use.

Is there any way to get the PA-80 do this (i.e. key on, pedal on, key off makes the note slowly fade away) with the damper pedal or the assignable switch?

How does PSR 2000 behave ?

Thanks
Shiral

Damper and sustain are the same thing .