Good question to start Swede.
All rifles have to have a method or mechanism to load the round.
The earliest were the muzzle loaders where the powder and bullet were pushed down from the muzzle with a ramrod, Next came the breech loader where a heavy plate was lowered at the rear of the barrel so a cartridge could be pushed into the chamber, the breech block was raised and the hammer cocked so you could fire.
Single shot or double barrel breech loaders or break action are still used. Mostly you will find them in shotguns and high end rifles used for extreme accuracy or in rifles chambered for very heavy hunting cartridges that produce pressures that will break many bolt actions, and are far too powerful for lever actions. Many are chambered for safari rounds for hunting elephants or other huge dangerous animals.
Ruger #1 is a single shot breech loader famous for its accuracy, and strength. It is chambered for most hunting rounds.
Lever actions work by having a tubular magazine. Developed during the American Civil war in the 1860s, the main attraction was that multiple cartridges could be loaded at once for firing instead of loading 1 at a time. Much faster. The rounds are loaded end to end and fed by a spring into position so that when the lever is lowered the bolt moves to the rear of the rifle and opens the breech. a spring lifts the cartridge into position and when the lever is moved back up to close it moves the bolt forward and picks up the cartridge and pushes it into the chamber ready to fire. When the round is fired, and the lever is opened again, the spent case is ejected so the next round may be picked up.
The original lever action was chambered for a pistol cartridge using black powder, low velocity, low pressures. Modern lever actions are made much stronger, but if chambered for an original round the cartridges you buy are downloaded to mimic original pressures so if you fire them in an original weapon, the weapon won't blow up in your face!
A bolt action is similar, except instead of a lever, there is a handle on the bolt and the basic actions are the same. You lift the handle, move the bolt back, and a round is picked up on the forward stroke when the action is closed.
Bolt actions may use pointed spitzer bullets that have better flight charicteristics as the cartridges are loaded into the magazine laying side by side instead of end to end.
As a bolt action usually has a stronger action they may use cartridges with higher pressures so higher velocities and speed which can improve accuracy. Usually a bolt action uses a heavier barrel as well to improve accuracy. Superb accuracy can be obtained with a bolt action that is modified to only shoot one round without a magazine. The bolt can handle very heavy rounds, but the action is long and increases the weight of the weapon.
Pump actions are a variation on the lever, but instead of the lever being located on the bottom of the rifle, you slide the pump which is the forarm of the weapon under the barrel. You move the slide back toward the rear of the weapon to open the breech, and move it forward to close.
There have been a few pump action rifles, but they were never really popular. Shotguns however use pumps in a big way. Very popular for follow up shots.
Semi Automatics are named thus because they automatically load a new round each time the trigger is pulled and a round is fired, The first round is loaded by "charging the bolt". You manually pull back the bolt to load the first round, but after that, each time you fire, some of the gas from the fired round is cycled back and pushes the bolt back to pick up the next shell.
Semi Automatics only fire 1 shot for each trigger pull. The weapons are usually heavier and bulkier in sporting calibers, but they do have a high rate of firepower. They are quick to shoot. and the followup shot is really quick, as fast as you can pull the trigger.
Full Automatics are machine guns and pistols. They work the same way as a Semi-Auto, except they fire as long as the trigger is depressed. A semi auto fires once each trigger pull, a full auto can fire a full clip, or belt up to 100 rounds at a time.
Full auto are closely regulated. Usually not available to the average gun owner.
Full auto is primarily used by the Armed Forces. They are limited in caliber choices, usually are not as accurate as bolt action or lever action, and use a LOT of ammunition.
For survival, the weapon you shoot best is what you should carry. A single shot in a medium caliber will put down most game very well. They are easy to clean and care for, very few moving parts to break. Simple.
A bolt action comes next. They need some care, more moving parts to clean, but have a greater rate of fire, are accurate, and have a wide selection of rounds available.
A lever action is usually chambered for slower heavier bullets. Very nice to carry, excellent rate of fire, decent accuracy. They do have more moving parts, and need more care to keep in top condition, but are fast and light to handle. Pump actions also fall in this category.
Semi Autos need a lot of cleaning to keep at top performance. They fire rapidly so second or third shots are super quick, accuracy is good for the first shot, but you need practice to bring the sights back to target well for a followup shot. Maintenance is the biggest drawback, and in hunting calibers, the weapons are heavier than a comparable bolt, lever pump or single shot. Accuracy can be good to terrible depending on individual weapon.
I would not consider a full auto as a survival weapon except in combat. Need a lot of care and training to use effectively, use a lot of ammunition, restricted availability, and usually not great accuracy. Some weapons do a good job, but a full auto is designed to fire a lot of rounds to hit multiple targets.
That concludes my tutorial, Firearm actions 101