A mocha is similar to a latte (espresso + hot milk), but with chocolate, added via cocoa powder or chocolate syrup. Think of a mocha as a grown-up hot chocolate.
This one doesn't need much explanation – black coffee is simply a mix of water and coffee! There's no milk or sugar added. (Unless you add it yourself, of course.)
Similarities
The main similarity is that they're both coffee drinks! They're both can be served hot or cold. That's about it! ;)
Differences
The main difference between mocha and coffee is that mocha is an espresso and coffee is not.
Caffeine
If you're comparing a regular one shot mocha and a cup of coffee, a cup of coffee has a bit more caffeine than the coffee. But the chocolate in a mocha might give you that extra sugar rush you're after!