There are five weapon types in Genshin Impact: Bow, Catalyst, Claymore, Polearm and Sword, each of theses have their own strength and weaknesses:
Bow: These naturally have the longest range with pin point accuracy from their Charged Attacks.
Catalyst: Catalysts come in either as a book form or an Orb form. The standout trait of these are that their normal attacks are Elemental damage based of the casters Vison.
Claymore: Claymores are the slowest weapon types but boast the highest damage. Their charge attack changes depending who wields it and will usually be some sort of continuous attack providing you have the stamina to use it. They also have bonuses to breaking Geo objects such as enemy shields and even ore nodes around the world.
Polearm: The fastest weapons in the game but they also have the lowest attack with better reach than the normal sword. There are only three characters in the game that use these currently and they are Xaio, Xiangling and Zhongli.
Sword: Swords are in the middle of the pack with their attack speed and damage sitting in between the Polearms and Claymores. Their Charged attacks are normally two rapid attacks although that can change depending on who wields it.
The weapons have a rating starting from one star to five stars and here is how they are found:
1 and 2 stars: Found from enemy drops, chests and purchased through NPC shops, these are mainly used as upgrade materials for the higher tiers.
3 stars: Found from chests and Wishes (Gacha)
4 stars: Found from Forging via the Blacksmiths and Wishes.
5 Stars: Only obtainable through Wishes.
There are two different types of forging in Genshin Impact, Ore Forging and Weapon Forging.
Ore Forging allows you to craft level up materials known as Enhancement Ore, these are used to level your weapons up to a certain soft cap where you will need to Ascend the weapon to continue leveling it. Ores are found around the world from Ore Nodes as well as sending your characters out on Expeditions from the Adventurer Guild.
Weapon Forging allows you to craft specific four star weapons providing you have the materials. This is usually a lot of Ore and a weapon prototype which drop from the weekly bosses.
Refining allows you to increase the weapons passive effect and will increase up to a maximum of Rank 5. This can only be done by providing the exact same weapon to reach the next rank, with the five star weapons feeling next to impossible to rank up due to their low obtain rate which is why a lot of people tend to go for the four stars in their place.
Weapons will usually have a unique ability on them such as the Skyward Blade for example, it has Skypiercing Might, and at Rank 1 this increases movement speed, attack speed by 10% as well as 20% damage increase for Normal and Charged Attacks by 20% for 12 seconds, to activate this powerful buff you need to cast an Elemental Burst. At its highest rank the 20% increase will turn in to a huge 40% for Normal and Charged Attacks.
At select levels your weapon will not be able to level higher until the weapon is Ascended (Leveled Up) with Ascension Materials. You’ll need to do this several times, one at Level 20, 40, 50, 60, 70, 80 and finally it will cap at level 90.