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.  This contrasts with a project manager, who manages individual projects. However, some organizations (particularly government entities) use the term program management, when they really mean project management.

More generally, whereas the term “project management” has a fairly common definition these days, “program management” often means different things to different people. (Some programs look more like operational programs than PMI-type programs.) In your particular situation, I would look at the job description carefully, and if your skills and experience are appropriate, I’d apply, regardless of what they are calling the position.  However, I might also include a cover letter mapping your background to the things they are looking for.

The terms “program” and “program management” are used in different ways by different organizations. Some organizations and industries refer to ongoing or cyclical streams of operational or functional work as programs. Other organizations refer to large projects as programs. These “programs” include large individual projects or a single large project that is broken into more easily managed subordinate projects. Because these efforts are more accurately characterized as projects—not programs—they remain within the discipline of project management and, as such, are addressed in the PMBOK ® Guide . When the management of these efforts results in the delivery of an individual or collection of benefits, and effective control is not achievable by managing the individual projects or components as separate initiatives, the effort may be defined and managed as a program as described in this standard.

Project Management Institute, Standard for Program Management