A renormalization condition defines a renormalized field or parameter by prescribing a correlation function at a chosen kinematic point. Changing that point changes the renormalized parameters while leaving physical predictions invariant.
A renormalized coupling is an interaction parameter defined by a specified finite renormalization condition or subtraction scheme at a scale . Observables remain independent of that arbitrary scale when its running and the loop corrections are included consistently. The coupling itself, and higher-order coefficients in its renormalization-group beta function, can depend on the scheme; they should not be identified without qualification with a regulator-independent bare coefficient.
A momentum-subtraction scheme defines renormalized masses, fields, and couplings by fixing correlation functions at specified external momenta.
The on-shell renormalization scheme fixes masses at physical propagator poles, fixes field normalizations by pole residues, and fixes couplings through amplitudes evaluated with external particles on their mass shells.
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