Exploit is to take advantage of someone - or to use them while they are weak.
Deprive is to take something away from someone. Like not paying your workers (or underpaying), or stopping food/water delivery into an area (siege.) Police will deprive you of sleep for interrogation (they do not allow you to sleep.)
You can exploit someone without depriving them. For example, can use someone to do something that they don't want to do (through coercion) BUT you can pay them well for it. In this case, you deprive them of dignity (self-respect) but not money. Most of the time, when people are exploited, they will be deprived of fair pay (or pay at all.) But exploitation and deprivation are not the same, even though they're related.
Generally, tycoons are seen doing both. They will employ desperate people and pay them very little - so it is both exploitation and deprivation. It is more complicated though - economically and philosophically.