You're right, they're not the same.
A nondisclosure agreement ("NDA") typically includes restrictions on both disclosure and use of the confidential information in question. A noncompetition covenant is sometimes used as a means of enforcing an agreement's use restrictions. It says, in essence, "to make sure you don't use our confidential information without our permission, you agree not to compete with us at all in the following geographic area for the following time period ...."
NDAs are commonly used to help two (or more) parties decide whether they want to do business with each other. As a result, NDAs per se hardly ever contain noncompetition provisions --- it's usually too soon in the parties' relationship for one of them to be making that kind of commitment.
Putting a noncompete in an NDA would be tantamount to a man and a woman agreeing to get a coffee to get to know each other --- and the woman says, oh by the way, I need you to agree that, for the next two years, you won't talk to any other women. Imagine the guy's reaction ....
A slightly different situation is when one company (the acquirer) is talking to another (the target) about a potential buy-out. When things start to get serious, the parties likely will sign a no-shop agreement that says, in essence, the target won't go looking for other potential acquirers. (The target's board of directors may have a fiduciary responsibility to its shareholders to consider other unsolicited offers.)