Those guys hit the nail on the head for sure.
One of the major difference aside from having guns is the leveling
First of all, XP and leveling. You get XP for killing enemies, picking locks, hacking terminals, completing quests, etc. All of that XP is counted towards the same thing - your level. It is much different since in Skyrim, XP you get from killing or whatnot is put into separate categories, then from there it is counted into your overall level. In Fallout, it goes directly into your overall level.
Also, skills are reversed. You do not level up your skills by exercising them, like in Skyrim. When you level up, you are allotted 15 points (that is the base, you can raise that with Intelligence) to distribute however you like into any of the skill categories. This is the only time you are able to put points into these skills. These skills help you boost your efficiency in that given area.
Basically, you can only raise your skills when you level up. Each point you put into a skill will increase you proficiency in that given field. Example, you put your 15 points into Small Guns (assault rifles, handguns, etc.). That allows you to deal more damage with weapons categorized as 'Small Guns'. In Fallout, skills affect you, you don't affect skills.
Perks are not in trees, and rather are listed. Each perk has a specific level requirement you have to meet before choosing a perk. Some perks also have a skill requirement, like one perk may require a science skill of 50 to choose. Once again, you may only increase your skills once you have leveled. You may only choose one perk per level, like Skyrim.
S.P.E.C.I.A.L. is also a huge difference. Special stands for -
Strength - lets you carry more, stronger with melee
Perception - better radar, enemy detection
Endurance - health, damage resistance
Charisma - speech, bartering, trading, etc.
Intelligence - increases amount of skill points available, some other effects
Agility - overall character speed, probably something else
Luck - critical hits and such
SPECIAL traits are ranked from 1 to 10, and you are able to set these to your liking at the beginning of the game. They each start at 5, and you have 5 or so points to put into them. You can also take points out, basically allowing you to pick and choose how you want the basics of your character to look like. A strong, melee guy? Put them in strength. A nerd? Intelligence, and so forth. You have opportunities to increase these with perks and gear that increases them, but this is the basis for your character.
Apart from leveling differences, weapons have durability. The more you use it, the more it wears down. In Fallout 3, you must raise your repair skill to repair weapons on your own. In order to do this, you need another weapon of the same kind you are repairing, then you can go into your inventory and repair one with the other. You also have the option of getting it repaired by a vendor, but I find that to get expensive fast.
Oh, and armor has durability as well. The more hits you take, the more it wears down. Same repair deal as weapons.
When something's durability reaches 0, you cannot use the weapon anymore. With armor, you can initially continue wearing it, but it does not protect you at all. It stays broken until you repair it, obviously.
Guns change the game quite a bit, as you need to keep track of ammunition. Different guns require different ammo, obviously.
Drugs are the Fallout equivalent of potions, except there is no alchemy, you have to buy them.
That's all I can think of off the top of my head, hope it helps. Just some major and minor differences.