A program charter refers to a document that expresses the program's purpose (mission statement), as well as its scope and participants. It may or may not explicitly represent a founding document.
The Merriam-Webster dictionary defines charter as "a grant or guarantee of rights, franchises, or privileges from the sovereign power of a state or country" or "a written instrument that creates and defines the franchises of a city, educational institution, or corporation." The common element is setting out the conditions under which an organized body is formed, its purpose in existing and the scope of its powers.
This is derived from examples, such as the "Charter for the United Nations" and "Magna Carta" charter from English history. These were documents that established a new organization and a new direction in governance. However, they share the similar aspects outlined previously, that of scope, goals and participants.
The term project charter has a very similar meaning in terms of identifying scope and objectives. The word "project" may or may not refer to something smaller or more limited in scope from a program. The implication from the latter word is something more ongoing, while the former is shorter term. However, this is not always the case.