Quantum Field Theory (QFT) and String Theory, including its different versions and related theories like M-theory, are distinct frameworks for understanding the fundamental nature of the universe.
QFT is a powerful framework that describes the behavior of elementary particles and their interactions in terms of fields. It is based on the principles of quantum mechanics and special relativity. QFT has been very successful in describing the behavior of particles at high energies, and it is the foundation of the Standard Model of particle physics.
On the other hand, String Theory is a theoretical framework that posits that the fundamental building blocks of the universe are not point-like particles but rather tiny, one-dimensional strings. These strings vibrate in different ways, and their vibrations give rise to the particles and forces we observe. String Theory goes beyond the scope of QFT by providing a consistent framework for incorporating gravity into quantum mechanics.
String Theory has different versions, such as Type I, Type IIA, Type IIB, heterotic SO(32), and heterotic E8×E8, each with its own mathematical formulation and set of properties. These different versions of String Theory arise from different ways of compactifying the extra dimensions of spacetime.
M-theory is an extension of String Theory that is believed to unify the different versions of String Theory. It incorporates 11 dimensions of spacetime (compared to the 10 dimensions in the original String Theory) and includes objects called branes, which generalize strings.
To answer your question, QFT is more general than the different versions of String Theory and related theories. QFT encompasses a wide range of physical phenomena and has applications in various branches of physics, including particle physics and condensed matter physics. On the other hand, String Theory is a specific framework that extends beyond QFT by incorporating strings and providing a consistent description of gravity.
In terms of inclusion, it is correct to say that all string theories are quantum field theories, as they involve the quantization of fields associated with the vibrating strings. However, not all quantum field theories are string theories. QFT is a broader framework that includes various field theories, such as the Standard Model, which are not based on string-like objects.