A cartridge, also known as a round, consists of a projectile, propellant, and a primer, all encased within a metallic or plastic casing.
Rimfire refers to a round that has the primer around the rim of the bullet, the firing pin does not hit the middle of the cartridge to ignite it is actually hits the rim where the primer is to ignite it.
.17 HMR - A rimfire round based off the .22 WMR. It shoots a 17-20gr .17 caliber bullet at around 2500 FPS and has super flat trajectory, making it a great round for varmit hunting at less than 200 yards. It was first made by Hornady in 2005,hence the name Hornady Magnum Rimfire (HMR).
.17 HM2 - The same idea that drove the .17 HMR, it is just a necked down .22lr to acheive the same princaples as the .17 HMR.
5mm Remington - This round was made in 1970 and is now obsolete. The round never became popular and rifles were no longer made after 1974.The round was based off of the .22 WMR and was made to hunt varmint due to the increased bullet speed and the .20 caliber bullet.
.22 WMR - The Winchester Magnum Rimfire is a rimfire round that fires a .22 caliber bullet at about 1800 FPS, and delivers a higher foot pounds than the .22lr. It was made for hunting prairie dogs and was based off of the .22 WMF.
.22 Long Rifle - The most common rimfire round. This round was made for small game plinking and is one of the highest selling rounds to date. It can be bought for very cheap and at near any store that sells ammunition. It has many variants, including: .22 Short, .22 CB/BB/CB Cap, .22 Long, .22 Extra Long .22 CB Long. .22 Stinger and .22 CAP. Despite the poor characteristics of the round is is very fun to shoot and hunt small game up to foxes with it.
-Update: All the .22LR is sold out everywhere. Turns out those crazy preppers bought it all.
Centerfire refers to the firing pin hitting the center of the round and making it go boom.
9x19mm - This cartridge, originally designed by Luger (hence the nickname 9mm Luger) for use in their pistols and later even submachine guns, is a common round today for a handgun to be chambered in. It is small enough that it will sail through a target, causing minimal damage. Also called 9mm Parabellum(Para bellum = prepare for war, from the famous catchphrase Si vis pacem, para bellum - If you want peace, prepare for war). This caliber was created after the .30 cal Luger bullet was deemed to small by military brass.
10x22mm (.40 S&W) - This cartridge was developed starting in 1990 from the get go as Law Enforcement cartridge and a stop gap to the FBI's rejection of the 10x25mm cartridge and the 1986 Miami Shootout. Becoming a large success in both the Civilian and Law Enforcement sectors. This cartridge has a performance range in between 9x19mm and .45 ACP. A standard 180 grain projectile has a velocity of 1,050 FT/S and producing 441 FT/LBS of energy. The 10x22mm is available in a large range handgun platforms and some submachine gun platforms.
7.62x25mm - This cartridge was made by Russian in 1930 for the standard issue TT-33 Tokarev and later the PPSH-41 and PPD-43. It shoots a .30 caliber bullet at around 1500 FPS and delivers about 400 foot pounds. This is a pistol sized round. It is also worthy of note that surplus for this round has dried up.
.45 ACP - The .45 ACP cartridge was created for use in the M1911 pistol. Because it is .06 inches wider than the 9mm cartrige, any target that the .45 passes through will be instantly and painfully obliterated as the large round pulls human limbs off with a single shot.
7.62x39mm - This round was made by Russia in 1943 as is an intermediate round that travels about 2400 FPS and delivers about 1500 foot pounds. This is the round used this the iconic AK-47 and SKS. This round still has an avalability of surplus.
7.62x54mmR - This is a full sized rifle round made for the Mosin Nagant. It was made in Russia in 1891. This round travels at about 2600 FPS and delivers around 2600 foot pounds. Surplus is widely available as well, coming in cheap spam cans of 440 rounds.
.303 British - This was the standard full sized rifle round for Britain. Made in 1904 it was for the Enfield based rifles. It travels around 2600 FPS and delivers about 26000 foot pounds.
30-06 - This round is a very common US made full sized rifle bullet. It was made in 1906 and was originally meant for the 1907 springfield rifles. It is very common round for large game hunting in the us. It travels at about 2700 FPS and hits with about 3000 foot pounds.
5.56×45mm NATO (official NATO nomenclature 5.56 NATO) is a rifle cartridge developed in the United States and originally chambered in theM16 rifle. Under STANAG 4172, it is a standard cartridge for NATO forces as well as many non-NATO countries. It is derived from, but not identical to, the .223 Remington cartridge. When the bullet impacts at high velocity and yaws in tissue, fragmentation creates a rapid transfer of energy which can result in dramatic wounding effects.
.51 Gyrojet - This round is exactly what it sounds like, .01 bigger than the .50cal. However, the key difference in the Gyrojet weapons was the in the fact that they were literally miniature rockets. While this sounds very complex like the clock-work steam-punk German master-race HK G11, it is actually rather simple. Pull trigger, bullet flies forwards, microjet activates, whoever is in front of you is missing a limb. While at point-blank the round was useless because the microjet wouldn't activate until ~30 feet, at longer ranges it worked very well. Low recoil, high speed, (low drag hurrdurr), it would have a been great concept, except for the $100 price tag, per bullet.
Tl;DR - mini rockets fly fast, big boom, too much money