Is it appropriate to apply for a program management position with project management related work experience?

In the PMI world, a program is a collection of projects that all have a common objective, and a program manager is therefore coordinating the projects across the whole program.  A project manager manages individual projects.  However, some organizations use the term program management, when they mean project management.

Whereas “project management” has a fairly common definition these days, “program management” often means different things to different people. In your particular situation, I would look at the job description carefully, and if your skills and experience are appropriate, I’d apply.