Think instead about electrical resistance. All of the following are true;
resistance = potenetial difference / current
resistance = resistivity * length / cross-sectional area
resistance = power disippated / current squared
But only one of these - the first one - is what we mean by resistance. This is the definition of resistance - the other equations just use this definition.
Of the four equations you give involving force, only one of them is the definition of force. I think that the problem here is that force is a term we use for a fair while in a "you know what I mean" way, before the definition is given - if the definition was given first, it would slow down the flow of most A Level courses, where you can do (for example) statics problems without having to worry about what a force actually is.
(The definition of force is wrapped up in Newton's second law.)