Yes, there is a lot of overlap. Theoretical physics really means non-experimental physics. In many areas of physics, both the theory and the experiments are so complicated that people have to specialise to master on of them. This division between theory and experiment is perhaps largest in particle physics, where the experiments are massive and the theory needs a lot of maths etc. However, there are also theoretical physicists who work in other fields such as quantum computing or physics of materials.
theoretical physics is a way of conducting research in which you use mathematics, equations and codes to simulate or model a physical situation. There are lots of equations that govern how particles move and behave under certain conditions in all areas of science, so we can use these to build a mathematical representation of what happens and what is observed in real life. There’s a lot of theoretical physics in plasma physics for example, as well as particle physics. You tend to find theorists in every department of physics actually, because there are so many equations and mathematical concepts that describe physical concepts. Maths is like the language of science. Particle physics is a department name that will include the experimentalists (people who test things out in the lab) and theorists (people working on simulation codes and the mathematics) who work together a lot of the time to write papers and figure out how to explain or predict what we can measure.
This is a good question. I have worked with experimental and theoretical physicists, but always specialists in particle physics. In general the theorists might work out some tricky calculations that predict the rate of a particular process, or perhaps deliver some interpretation of the experimental data that tells us about the structure of the proton.
The result of the theoretical work is often quite complex, and a good way of communicating the results of those cutting edge calculations to experimentalists is to write a computer simulation of the process(es). Experimentalists can then use that simulation to produce “fake” collision events, the outcome of which is a set of fake particles exactly as we would see in our detector. The fake particles can then be analysed as if it were real data, without needing to know the precise details of the calculation.
It is actually very important that experimental and theoretical particle physicists are able to communicate – sometimes it can feel like the two areas are too separate.