FEM is a “mathematical method” for solving problems of engineering and mathematical physics that involve complex geometries, loads, boundary conditions, and material properties. FEA is the “practical application” of FEM to simulate the physical behavior of a system or structure using software.

The basic principles underlying the FEM are relatively simple. Consider a body or engineering component through which the distribution of a field variable, e.g. displacement or stress, is required. Examples could be a component under load, temperatures subject to a heat input, etc.

It is very much is a school/instructor specific thing, difficulty-wise. Basic FEA is pretty straightforward, but it can get complicated, and people having been doing PhDs on FEA methods for 40+ years.

FMEA vs FEA It is commonly used in engineering to simulate the behavior of structures, components, and systems under various conditions. However, FMEA is focused on identifying and mitigating potential failure modes, while FEA is a computational method for analyzing the behavior of physical systems.