to serve as a slave: to belong to a master and give the obedience and labor a slave owes him
This is the verb behind the noun for a slave. It does not mean simply to help out or to lend a hand; it means to be someone's property and to do the work that being owned requires. So wherever the New Testament uses it, there is always a master in the picture and a person bound to that master's will.
The striking thing is that the word itself carries no praise or blame. What decides everything is who the master is. The very same verb describes glad, wholehearted service to God and hopeless bondage to sin, money, or appetite. Paul builds a whole argument on this in Romans: no one is truly free and master-less; you are a slave either to sin, which pays out death, or to God, which leads to life. The choice is never whether to serve, only whom.
Because of this range, English has to reach for different words. When the master is God or a fellow believer, translators say serve; when the master is sin or a false god, they say be enslaved or be in bondage. It is one Greek word doing all of that work, and the shift in English tells you the master has changed, not the verb.