Early Bullets, prior to the American civil war thereabouts, were typically soft lead. That is they were basically pure lead or an alloy that was just slightly harder than pure lead. That was ok because the large caliber bullets used in early guns were not intended to be loaded to anything over maybe 1000 feet per second. At those low velocities and large bore sizes soft alloys worked just fine. In fact the mini ball of civil war fame relied on the soft lead alloy to function. As the black powder burned under the bullet, the hollow base expanded and sealed the bore from the gasses.
At the end of the 19th century an absolute revolution in small arms ammunition occurred. Black powder, which had been the only powder since the invention of the gun, was replaced by smokeless powders which are made from nitroglycerin, nitrocellulose, or a combination of both. Along with this change in powder came changes in cartridge design. Metallic cartridges had now replaced muzzle loading and other tedious loading procedures. The self contained metallic cartridge was at first used with the same old black powder. When they started loading them with smokeless, it was a marriage made in heaven.
Black powder could only create so much pressure, so therefore the bullets used with it were rather large. Big bullets traveling slowly (600-1000 fps) do a lot of damage. But with smokeless powders you can create great pressures and do the same damage with a smaller bullet. Instead of a .50 caliber bullet doing say 600 fps. You now had a .30 caliber doing 2000 fps. The problem became that lead bullets just could not with stand the speeds they were being propelled at. Enter the jacketed bullet. We'll learn more about that later.
Here is the low down.
Alloy is the term used to describe a mixture of metals. Pure lead is very dense and works well in low speed antique applications. However it just does not perform in smaller, faster applications. leading of the bore is one issue. One way to avoid the inherent problems of lead bullets is to mix the lead with other metals to make an alloy that is harder than pure lead. These bullets are often termed "hard cast" bullets. Metals like antimony and tin are added to the lead. The resulting alloy is much harder than lead and perform well up to a point. Unlike pure lead there is little or no deformation or expansion when hard cast bullets strike a target. Like lead bullets, hard cast bullets need to be lubricated and as such will have grease groves to hold lubricant.
Hard cast bullets work well in pistols of all types as well as rifles, so long as they are loaded to an appropriate speed. Cast bullet loads often use powders designed for pistol and shotgun work. One way of getting more speed out of a cast bullet is the use of a gas check. Simply put, gas checks are copper or other soft metal attached to the bottom of a cast bullet that resist the burning powder's heat and pressure.
Most modern factory bullets are of the jacketed variety. Indeed, you just can't push cast bullets at the velocities developed in modern rifle loads, weather gas checked or not. Jacketed bullets are made differently than cast bullets. The jacket is usually made of copper. Think of it as a gas check that covers the whole bullet. What we see is actually just the jacket. The lead is inside. It is not cast, but cut from a roll of soft lead wire and inserted in the copper jacket. Here are some terms you need to know.
Full metal jacket. The jacket encloses the entire bullet. These may or may not have an exposed lead base, but the sides and top of the bullet are enclosed in copper.
Hollow point. These bullets have a cavity at the top which cause the bullet to expand when the target is impacted. This design stops over penetration.
Soft point bullets have an exposed soft lead tip that deforms and mushrooms upon impact. Like a hollow point, they aim to stop over penetration and deliver the kinetic energy to the target.
As you have probably noticed, bullets come in all shapes and sizes. Flat point, spire point, wad cutter, semi wad cutter. The nomenclature can be confusing. All designs have a purpose. Some are appropriate for pistols but not rifles, Some are great for varmints, some self defense. Some are for big game. It all depends on what you are shooting it out of and what you are shooting at. I've included some pictures of different bullet designs.
Have you contemplated digging that old .410 out of the closet only to choke to death on the price of shells? The current price for AA target loads at my local wal-mart is right around $12. If you want anything other than that, the price goes up to about $16. That's pretty disgusting when you consider I can buy a 100 round pack of 12 gauge shells from the same shelf for $22. Let's see that's $.48 per round for .410 and $.22 per round for 12 gauge. $.48 a round doesn't seem like much to a rifle shooter, but to a shot gunner it's murder. A typical 12 gauge target load has 1-1/8 oz of shot and somewhere around 18-20 grains of powder whereas a .410 is only a 1/2 oz of shot and maybe 10-12 grains of powder. They both use the same 209 primer. Heck, even the plastic wad and shell takes less material. 
