  It is demonstrated that the renormalization group (RG) flows of depinning
transitions do not depend on whether the driving force or the system velocity
is kept constant. This allows for a comparison between RG results and
corresponding self-organized critical models. However, close to the critical
point, scaling functions cross over to forms that can have singular behavior
not seen in equilibrium thermal phase transitions. These can be different for
the constant force and constant velocity driving modes, leading to different
apparent critical exponents. This is illustrated by comparing extremal dynamics
for interface depinning with RG results, deriving the change in apparent
exponents. Thus care has to be exercised in such comparisons.
