What are the basic differences between a grand unified theory (GUT) and a theory of everything (TOE)?

A Theory of Everything (TOE) is a theoretical framework in physics. Its goal is to unify all known physical phenomena within a single, all-encompassing theory. This means it seeks to explain and intertwine all four fundamental forces of nature:

• Strong nuclear force
• Weak nuclear force
• Electromagnetic force
• Gravitational force

Currently, gravity is a major challenge when it comes to unification, as it is successfully described by General Relativity, which doesn't easily mesh with the other three forces, which are effectively explained by Quantum Mechanics.
A TOE is more ambitious than a Grand Unified Theory (GUT) because it aims for a comprehensive explanation of the fundamental aspects of nature. Successfully achieving a TOE would mean understanding everything from the smallest particles to the vast cosmos.

In physics, fundamental forces are the basic interactions that do not appear to be reducible to more fundamental interactions. There are four fundamental forces:

• Strong nuclear force: This force holds the nuclei of atoms together and is the strongest of the four, but operates over a very short range.
• Weak nuclear force: This force is responsible for radioactive decay and neutrino interactions. It has a very short range and is weaker than the strong force.
• Electromagnetic force: This force acts between charged particles. It is responsible for electricity, magnetism, and light. It has an infinite range but is weaker than the strong nuclear force.
• Gravitational force: This force is the attraction between masses. It is the weakest of the four forces but acts over an infinite range.

Each force is associated with fundamental particles exchanged between matter, known as force carriers, such as photons for the electromagnetic force and gluons for the strong nuclear force.

Theoretical physics focuses on developing mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. It operates through:

• Formulating physical theories
• Using mathematics to model physical systems
• Predicting outcomes of experiments

Large areas within theoretical physics include:
Quantum Mechanics: Describes nature at the smallest scales of energy levels of atoms and subatomic particles.
Relativity: Encompasses both General Relativity and Special Relativity, where space and time are intertwined, affecting gravity and high-speed motions.
Theoretical physics is crucial for seeking unifying theories like GUTs and TOEs, integrating our understanding of the universe at both the cosmic and particle levels.