A moneyline bet allows you to pick a winner straight up regardless of who is favored. But the amount you win, relative to your bet, will be less if you bet on the favorite than if you bet on the underdog.

A bet against the spread allows you to bet on a winner, but against a "handicapped" score.  The spread is the amount of points that the favorite team has to win by in order for your bet for the favorite team to pay out.  Conversely, you will a bet for the underdog if that team either loses by less than the spread or outright wins.

 This article does a pretty decent job explaining it.