It's not as simple as "they're not the same plant"; it's more like they can be different varieties of the same plant, or the same plant raised under different conditions. For example, all pure sativa strains, including those grown mostly for drugs (e.g., Thailand's classic) can easily reach fifteen feet if allowed to do so, making them at least decent for hemp fibre.
Take the same plant, cullthe male plants, grow it under strong lights that are drastically curtailed after six weeks' time, and you get a perfectly good drug plant (perhaps not of super-potency, but the quest for super-potency is a bad artifact of the W.o.S.D., for which see the growth of hard liquor over beer during Proinhibition).
All varieties can freely interbreed with each other, and in fact a burgeoning hemp industry could be very bad for pot growers if the level of hemp pollen grew too high.
I think the "they're not the same plant" meme is an attempt to get past the bigfella tabu-tabu nature of the word "marijuana"...for example, imagine all your best pro--mediical-marijuana arguments with "marijuana" replaced with "baby heads", and you'll understand the opposition better:
Me: But baby heads have proved to be effective against nausea!
Him: But...it's baby heads!!! We can't even think of using them.