The parameters of the Standard Model (SM), as the particle’s masses and the interaction couplings, are very special. They encode the notion that interaction changes the properties of the free particles by absorbing some divergencies that show up when computing basic processes in the SM. The formal definition of the SM parameters is determined by the way such divergencies are absorbed. But as long as one stay within the SM, all those possible definitions can be easily connected.
The top quark is the heaviest particle in the SM, which motivates the measurement of its mass from many different processes and observables. The most precise top quark mass measurements rely on Monte Carlo simulations, where certain aspects related to the top quark fragmentation, decay and hadronization are modelled in such a way that the top mass cannot be systematically controlled from first-principles. The discussion about the interpretation of the top quark mass is open.