It's completely different in my opinion, the only similarity is that you have two people and one computer.

In pair programming you're both working together, complementing each other to tackle a particular problem or issue. In a good pair programming session we'll both work together to surpass an obstacle.

In an interview, one person is observing, testing and ultimately judging the other person, while actively ensuring they do not contribute to the solution of the problem so as not to skew results. Only one person is truly working towards the programming goal, and both participants know this.