The general idea with regards lifting weights is to associate this with bodybuilding, instead of the proper weight lifting with regards powerlifting or Olympic lifting.
It is true without the influence of Arnold Schwarzenegger and the old lads of bodybuilding we would not have the great lifting culture that we have now as they were a great driving force and a massive influence on anyone who wanted to chuck some tin around and deserve a massive amount of credit.
With most sports, MMA, boxing, judo, rugby, it is not always about size, sometimes in these sports the bigger muscular guys, tend to be to heavy and lack conditioning.
If you are training for sport or training to get powerful and strong, your programme should revolve around increasing performance, by using more compound movements whilst trying to increase the force you proudce as this in turn will make your stronger and also develop an atheltic phsyique as long as the nutrition is on point. Therefore training like a bodybuilder with split body part routines and isolation work, is not the way to do it.
An athletic physique is that of an MMA fighter (See above), slight and strong or a strongman, big and strong (See below).