Caption: A schematic diagram of the branches of physics: i.e., the REALMS of physics.
The diagram only gives a rough idea of the relationships of the branches It is meant to be suggestive. It takes many words to give a more exact understanding of the relationships---and different people would give somewhat different understandings.
The diagram actually should have another dimension suggestive how emergence plays in---but that seems too tricky to illustrate---and so we will only discuss that below.
The theory of the branch can be regarded as an exactly true emergent theory in the limit of the branch. The branch and the branch theory have the same name and the two designations are often virtually synonyms since one usually means both when one gives the name.
The branch theories:
TOE encompasses all the other branches---they are emergent theories in the narrow definition of emergence (as given by, e.g., Wikipedia) as well as in the broad definition of emergence (as given by yours truly).
The other branches contained in the TOE branch can be reached by taking TOE to the appropriate limiting cases.
Classical physics is a vast branch.
Before circa 1900 it was thought that maybe it was all of physics. This was NOT a very perpsicacious view since all material properties had yet to be understood. However, probably people then thought of material properties as being NOT physics---maybe they thought of them as being chemistry---but physicists were darned if they were going to leave material properties to chemists.
Newtonian physics (AKA classical mechanics) is the low-velocity limit of the special-relativistic mechanics.
Quantum mechanics is essential to understanding atoms and molecules and how macroscopic material properties emerge from atomic and molecular behavior.
Modern electronics and your cell phone depend on quantum mechanics.
Newtonian physics is considered to be the macroscopic emergent limit of quantum mechanics. But, in fact, how it emerges in all perspectives has NOT yet been shown to the satisfaction of all people (see, e.g., Schlosser et al., 2013, A Snapshot of Foundational Attitudes Toward Quantum Mechanics).
Among many other things, quantum field theory is essential to understanding the interaction of electromagnetic radiation and matter.
Quantum mechanics can be understood as the low-velolcity or low-energy emergent limit of quantum field theory.
Special relativity Newtonian physics are the weak gravity emergent limits of general relativity.
General relativity is NOT consistent with quantum mechanics, and this is one of the reasons we know our current physics don't amount to TOE or TOE-plus.