Dr.Mario was very different to Mario functionally. Mario was an all rounder while Dr Mario was an aerial based character (he had much faster air control than Mario) with powerful attacks (particularly his fAir which is WAY stronger than Mario's and is a potent kill move and his nAir which is unique because it GAINS power the longer it is out, so throwing it out early and hitting with the late active frames was a good idea, because even if they jump at you, you have active frames out).
Dr.Mario had far worse recovery, his cape was much slower and had a much more narrow hitbox but much more range, also didn't bounce him in the air like Mario's did.
His Pills bounced low along the ground differently to Mario's allowing him to control the ground and then get into the air to abuse his powerful air game.
In Smash4 he could retain the Tornado while Mario has Fludd, further differentiating them.
Honestly, none of the clones in Melee were anywhere near as blatant as people think, because their moves are aesthetically similar, people assume they play much more alike than they actually do.