Many fish grow at different paces. Fpr example, clown loaches and plecos grow relatively slowly while most gouramies and guppies grow realy fast. A lot of it depends on the food they eat and the conditions they live in. Higher temperatures also speed up metabolism which makes them grow faster.
With injuries or barbels/fins the same factors will efect re-growth : water quality, feeding and temperature.
Healthy fish will always grow faster than sick fish and fish in a larger tank will reach their full size while those in small inadequate tanks can be stunted (their internal organs grow but their body does not ... ouch!).
