There is the Systems Framework for Personality Psychology, and there is systems thinking, and then, there is General Systems Theory (sometimes shortened to Systems Theory). They sound a lot alike, and so it is natural to associate them in one's mind.
Systems Thinking
Most scientists -- most people today -- use systems thinking. That is, they think in terms of systems. They recognize that many things, be they schools, river otters, televisions, or personalities, are systems. By system, in this sense, is meant a group of parts that work together in an organization. A given system (e.g., river otters) is embedded in a broader system (e.g., an ecosystem).
The Systems Framework represents this elementary sort of systems approach to a thing -- in this case, the personality system.
General Systems Theory
There is also, however, General Systems Theory, which is also sometimes called Systems Theory. Both terms can be used loosely. General Systems Theory takes as its operating assumption that systems at most levels of complexity share certain characteristics. For example, they may use feedback loops to regulate themselves. Or they may share certain other structures in common. The idea is that some general principles of systems can be applied to all (or almost all) systems.
The Systems Framework for Personality Psychology and How it Differs from General Systems Theory
The Systems Framework for Personality Psychology is not a part of General Systems Theory, except perhaps in the most limited sense that it purveys the idea that many systems can be studied by identifying the system, and then understanding its parts, organization, and development.
Using the Systems Framework to study personality does not commit one to the idea that personality should be studied as a system that shares certain general principles with other systems. That is an idea of General Systems Theory. Although General Systems Theory has offerred the scientific world a number of very interesting and important ideas, it is also true that personality has a number of quite unique features (as do most systems), and that scientists within the discipline need to spend their time, to a great extent, in understanding those unique features of personality.
That is a key place that the Systems Framework and General Systems Theory part company. That is, the Systems Framework considers personality to be a largely unique system. To study it, one must develop a language tailored and suited to the topic (Mayer, 1993-1994). Again, this is not to deny that General Systems Theory may offer important ideas to the field based on generalizations across systems.
The Systems Framework does provide coverage of General Systems Theory. In its "Introductory" topic it covers a variety of theories including the psychodynamic, humanistic, cognitive-behavioral, and many others -- including General Systems Theory. As with any of those theories, the Systems Framework draws on aspects of General Systems Theory when it can illuminate a key idea particularly well (as in, for example, the case of self-regulation and feedback loops). In other words, General Systems Theory is a legitimate member of the theories that help inform personality psychology, but it has no special status within the Systems Framework.
Mayer, J. D. (1993-1994). A System-Topics Framework for the study of personality. Imagination, Cognition, and Personality, 13, 99-123.