I'll clarify this right here, right now.
There are two major types of ammunition in circulation today, for civilian purchase. There's some others, but for this purpose I'll ignore them.
First, we have FMJ. It stands for Full Metal Jacket. It's basically a piece of lead coated in brass or copper, or some mixture of the two, completely around the bullet itself (I'm not talking the casing, but the bullet itself). This causes the bullet to be extremely hard. If you shoot someone with an FMJ round it is going to pass through them in all likelyhood, and could very well cause the person to stay alive simply due to the lack of "knock down" power. To give you an example, I fired a .40cal FMJ through around 8 inches of wood, dug the bullet out, and it had barely even deformed at all. To injure/stop a person, you want the maximum amount of distortion of the round itself possible.
The second and most common self defense round is called a JHP, jacketed hollow point. It's the same as an FMJ but the tip is hollow, as you all know. This causes it to spread open (and actually break off fragments of the round itself) when it hits it's target. The good news, it rips the hell out of whatever it is (assuming it's relatively soft) and stops them in their tracks. While it's not completely uncommon for a JHP to travel THROUGH someone, it is LESS common than an FMJ doing so; and even if a JHP *does* pass through the person it will cause a lot more damage to the person in the process. *That* is why JHP's are ideal for personal protection.
JHP's do have a downside though, a lot of firearms have a hard time loading them; so they created a round called the EFMJ, expanding full metal jacket. It does the same as a JHP but it looks like a regular FMJ (for all intents and purposes), so it loads into the firearms without any issues and still expands upon impact like you would want.
Contrary to popular belief, JHP's are not illegal and anyone can buy them and use them as necessary for self defense.
And to blackmagic.
You're correct as well about your interpretation of Hollow Points.
However, on the "cheapest you can find" ammunition, I would beg to differ. I for instance, can't shoot anything other than a nice 180GR Winchester .40 round or 115GR Winchester 9mm with any sort of regular accuracy. IF I use any other "cheap" ammunition, I get irregular results. To let you know though, Winchester stuff in boxes of 100 at Walmart is $10 for 9mm and $15 for .40 - QTY:100. That's really cheap, and it's quality ammo.
FMJ: (after impact)
http://www.allsafedefense.com/images/Bullets/FMJ.jpg
JHP: (after impact)
http://www.allsafedefense.com/images...eerGoldDot.jpg
EFMJ: (after impact)
http://www.allsafedefense.com/images...on&Federal.jpg