They are very similar, of course. And sometimes, they can be used interchangeably. However, there is a slight difference.
"walk to" means to go somewhere, but it doesn't necessarily reference a specific spot and it doesn't say anything about what you will do when you get there.
I will walk to school. (But then I will walk to my first classroom.)
"walk up to" has a feeling of going to a specific spot for a defined purpose and stopping.
Walk up to that man in the park. (He will show you where to find the statue.)