If you somehow mean a "pure" copper-jacketed (or cupro-nickel) bullet, I can say this, almost directly out of Hatcher's Notebook.
With the early high velocity almost pure copper-jacketed or cupro-nickel bullets in cartridges like the .30-06, copper fouling up near the muzzle (where the velocity was highest), was the biggest nuisance and took a lot of study by the Ordnance Department.
In the meantime, various lubricants were used by match shooters to alleviate the copper fouling problem and every shooter had a little can of his own favorite lubricant at his shooting position, into which he'd dip the bullets of his cartridges before loading.
We ultimately found out that the French had been using thin strips of tin in the powder of their artillery pieces for years to avoid this problem, so we started to make powders with a certain amount of tin in them. These powders were numbered the same as ordinary powders, but had a "1/2" designation added to indicate the addition of tin.
At one point a lot of National Match bullets were actually tin-plated, and it was a very accurate lot, but it was withdrawn for other reasons.*
Finally, we decided to use a copper-tin alloy in the bullet jackets. I believe this was called "Lubaloy."
The thing is, that the different colors of the yellow brass case versus the copper-ey color of the bullet is simply because they are two different alloys of copper. It's just that one looks more like a penny and the other looks more like gold.
One (for the "brass" case) is designed to take the pressure of firing, still allowing the appropriate expansion to seal the breech, and then to spring back to allow extraction.
The other (for the "copper" bullet) is designed to "take" the rifling, then exit without leaving a deposit, and (in the case of game bullets,) expand properly.
Fortunately, there is enough latitude in all kinds of copper alloys to be able to meet both very different sets of criteria.
Traditionally, copper and tin make bronze, and copper and zinc make brass, but there is nothing graven in stone about this and I would bet that "brass" bullets are of an alloy which contains tin anyhow, and the "copper-ey" bullets are just an alloy which satisfies the "bullet" requirements better. But copper is getting pretty expensive, so there might be a motivation to reduce the copper content of jacket material nowadays, so they look more "brassy."
There is always some confusion about copper alloys, though:
http://en.wikipedia.org/wiki/List_of_copper_alloys
See also:
http://en.wikipedia.org/wiki/Gilding_metal
I have seen some comments that "brass" bullets with the same load and weight are slower than "copper-ey" ones and I would hazard a guess that since "brass" is harder than the "copper" jackets, it takes more energy to engrave them, possibly causing erosion at the throat of the barrel. And they might not slip down the barrel as easily as the so-called copper ones and therefore might cause more wear.
I don't know if SAAMI has done studies on this.
Terry, 230RN
*As it happened, while these "tin-can" cartridges were very accurate, the tin-plated bullet had a tendency to cold-solder itself into the neck. No problem, since the pressure of firing would easily expand the neck and release the bullet, and off it would go. But even though competitors were cautioned to not use grease on this ammunition, people still did. Thus, the layer of grease which got on the neck prevented this expansion-and-release of the neck and very high pressures were encountered.
REFs:
Hatcher's Notebook, in "Gun corrosion and ammunition developments." (I did not re-read this chapter, I'm working from memory here.)