Can I use the terms coupling constant and strength of interactions, interchangeably, or are there more subtleties to the term coupling constant that I am not aware of?
Coupling Constants from Wikipedia:
In physics, a coupling constant or gauge coupling parameter is a number that determines the strength of the force exerted in an interaction. Usually, the Lagrangian or the Hamiltonian of a system describing an interaction can be separated into a kinetic part and an interaction part. The coupling constant determines the strength of the interaction part with respect to the kinetic part, or between two sectors of the interaction part. For example, the electric charge of a particle is a coupling constant.
I am (in general terms) aware of the such concepts as running constants, fine structure constants etc., and their implications and uses in physics and it may be that the answer is simply that: if I can follow the complete Wikipedia article cited above, then that is "all" there is to it and I would be happy to be told that.