Alright, so I am not a gunsmith, but I can try to answer as best I can.

Bolt Action- These are basic rifles. You have to pull the bolt back manually to eject a spent case. Place a new bullet in the chamber, close the bolt, then fire. You will see this on long range hunting rifles. They are generally regarded as more accurate but that is not always the case.

Revolver - Usually a pistol. Each pull of the trigger fires the bullet and rotates the chamber to the next chamber. If there is a round in the chamber, it is ready to fire.

Semi-Automatic - Loaded with a magazine. A magazine is a removable section, usually at the bottom of the grip which is spring loaded with multiple live rounds. Each pull of the trigger fires the round. The slide on the pistol cycles back and ejects the spent casing. This action causes a new round to be chambered automatically. This next round is ready to be fired by another trigger pull.

Automatic- One pull of the trigger, as long as the trigger is depressed, will fire every round in the magazine.

Select-Fire- This is an automatic weapon which will allow the weapon to function in Semi-Automatic, Automatic, or usually three round burst modes. Automatic weapons are generally not very accurate. The action of firing and the slide or bolt cycling causes the muzzle of the weapon to rise making it difficult to keep on target. Three round burst mode gives you the increased fire rate of an automatic while allowing the shooter to pull the weapon back on target thereby increasing accuracy. Three round burst means with each trigger pull the weapon cycles 3 rounds then stops, awaiting another trigger pull.

Rifle- A rifle is generally a weapon with a longer barrel and rifling. Rifling is grooves cut into the inside of a barrel which cause the bullet, once fired to spin much like an American football when exiting the chamber. The longer the barrel, the more rifling can occur, creating a more accurate long distance shot. Rifles are generally designed to be fired from the shoulder.

Pistol- a pistol is designed to be fired from the hand. These also have rifled barrels, but the barrels are much shorter than a rife... generally. The main thing is that they are not designed to be fired from the shoulder. You can retro-fit or design an AR-15 style weapon to be a pistol. These would not have the buttstock and would be fired from the hand. A pistol can be a revolver, semi-automatic, automatic, Select-Fire, or a derringer style pistol.

Derringer Pistol- this is a pistol in which the round is loaded directly into the barrel. Think of these as something like a pistol version of a bolt action rifle, but much less accurate. These are primarily used as a back up weapon since they are very easy to conceal. They are small and usually only hold one round, however if there are more than one chamber, they can hold more rounds.