The sub-fields of electrical engineering are not that different. Electrical engineering is about two things:
a) Maxwell's equations.
b) Mathematical Methods to use those equations.
This can be clearly seen if you do a course in Microwave Engineering, and if the course covers Maxwell's equations, capacitance, inductance, and how they are related in transmission line and waveguide theory.
After covering Microwave engineering, it becomes obvious that a significant crossover exists between the following electrical engineering specialities:
1. High Power - Transcontinental power transmission lines follow the same rules as microwave transmission lines. It is just the geometry and wavelengths are far longer.
2. Motor Drives - Same inductance and capacitance problems, particularly when dealing with high-frequency switching power supplies driving much slower motors through cables. Ferromagnetism shows up in motor drives.
3. Power Supplies - Same as motor drives. Strong resemblance to AC/DC and DC/AC power conversion in high power electrical grid systems.
4. Circuit board design - Modern high-frequency circuit boards are all about transmission line theory.
5. IC design - Change the materials. All the theory is back again. Now you are applying Maxwell's equations at much smaller scales.
6. RF design - This is exactly what the microwave theory course is about.
7. Laser and Opto-electronic design - Maxwell's equations are back again. Frequencies, electron voltage changes, etc.
Electrical engineering is about two "simple" subjects: Maxwell's equations, and mathematical methods. Most electrical engineering projects devolve into a combination of:
a) something involving electro-magnetic theory and/or it's formal mathematical solutions, like Laplace, z-transform, Fourier Theory, and Wavelet theory, and
b) something involving Boolean logic, and/or implementations of Turing machines.
Electrical engineering is different from the rest of the engineering fields. In Electrical, there is only the four Maxwell equations, tons of mathematical abstractions, simplifications, solutions, methods and techiques, and all of the implementations and ramifications of the them. For Mechanical engineers, there is no set of unifying equations. Chemical engineers have VESPR and thermo-dynamics, but that only goes so far. Aerospace engineers have a set of CFD assumptions, but those assumptions only hold in gases, and get strange when chemical reactions and/or phase changes are involved. Civil engineers have a basic set of equations to cover the simple stuff, but the complex problems involve sophisticated mechanical engineering. In Engineering Physics, they cover the electrical stuff, plus the quantum equations (which are a mess.) Electrical engineering is the only field of engineering with only 4 equations, and tons and tons of math to simplify their solutions.