What Is a Subproject?
Like a project, a subproject is:
IBM uses the term subproject to refer to a part of a project managed with a level of independence.
What Is a Program?
The Worldwide Project Management Method (WWPMM) defines a program as a group of related projects and other activities managed in a coordinated way to achieve a common long-term objective.
A program is realized through multiple projects and ongoing activity. The scope of a program might be broadly defined and might evolve as the business or organization develops, or it might be specifically defined to achieve an agreed set of goals.