TMJ Total Metal Jacket Trademark fo Speer Bullets, so no one else can use the name, thus the CMJ is a generic name for the FMJ bullet with bases coverd.
CMJ is not the frontier bullet, but often confused. It's an electroplated bulleted, or encapsulated with soft copper (not alloy) over either a cast or a swaged core,
FMJ is term listed in the SAMMI definitions, and is often used with rifle ammo as well. Europeans have been covering the bases for years, reduces airborne lead, doesn't increase drag, or pressure.
The alloy of the core has more to do with pressure than the jacket material. Many use a soft core, reduces the amount of rifling formation, or swaging action and gasses bypass the bullet and accuracy falls off. One commercial manufacutrer used a pure lead core in FMJ and the bullets wouldn't hit the paper, they went all over the place. So, it's not quite as simple as many think, often there's propriatory rights, and other factors, etc.
Copper washed is different again, and then there's a cold plating and hot plating. Hot plating is brittle and prone to flaking, cold has advantages, but many can't do this.
We have cold plated bullets, swaged alloy cores,, (not cast) and of course the Montana Gold FMJ and CMJ's which are about as good as it gets.
Hope this helps clarify a few things. Oh, also the thickness of plating or jacket material, is of consideration, and how many draw process to draw out the cup, and how many finishing stamps to make them concentricical (spelling) electoplating isn't always consistent from side to side, and many plated bullets are not stamped after plating, thus they cold be out of round. But, it's all what you are after, just shooting, or going for the best possible score or target possible. There's a difference in quality and with that, there's a difference in price as well.
Now, are you confused? lots of insite, hope this helps.
Kurt @ canadianbdx.com, Canada's Montana Gold Bullet Distributor.