This is a general question to try and understand conceptually (in laymans (i.e. engineers) terms) the differences between the above solution methods for things like solving ODEs and PDEs. For context, I have done work in the CFD industry, and so am familiar with discretization schemes for FV-based CFD and FEM, and so am comfortable with how in most discretization methods, we end up with linear systems like $Ax=b$ which we need to solve (with things iterative solvers, Gauss-Seidel, conjugate gradient methods etc) but can't seem to understand how the Runge-Kutta methods fit into the mix.
For context, I am not looking for an indepth explanation of each kind of RK method as I can read this up myself, but more conceptually how they differ from the `normal' solution methods for systems of linear equations. Hopefully thats not too broad a question.
Thanks very much.