No, it's the notion that you have second-class citizens or even non-citizens with limited legal rights enforced by the state, said limitations usually being in the realm of property rights, personal freedoms, etc. At least that is fairly easy to define, whereas "grossly under compensating someone" is a vastly more nebulous term (who decides what is and isn't "under-compensating"?)

At its essence slavery is complete ownership of another person. Whether or not you put that person to "work" is a separate issue.

Try starting with the textbook definitions. Pretty much the defining factor of being a slave is that you are owned by someone else and have to follow their orders. You can be highly compensated and still a slave (see the myriad of anecdotes about “kind” slave owners who paid them well).

If a gang of armed men kidnap, brand, and return you, you're enslaved.