Weapons come in many different forms, and these forms determine the types of attacks the perform as well as if they are ranged, fire projectiles, or what have you.
Weapons
When you think of Weapon Types, you think Swords, Axes, Bows, etc. These are all present as are a bit more.

Here's a somewhat old example of Alton swinging a 1 Handed Sword. Version 0.5.x
Before we begin, there will be some terms used that need to be defined. These include Weapon Attack Types which detail how targets are picked when attacking, basically what and where these weapons can be used.
Weapon Attack Types
These make up the core differences between the many weapon types. Weapon Attack Type (or WAT) determines what tiles will be "in range" when you go to use the weapon.
Melee

Melee Two

Melee Eight

Ranged

Minimum range is something unique to Ranged WATs however not all of them have a minimum and some will allow you to attack adjacent tiles.
Ranged WATs are unique in another way. Since they often have a projectile that is fired, the path this projectile takes can differ greatly.
Ranged Indirect
For weapons types like Bows, projectiles are fired in a parabolic arc, allowing them to hit targets that are not in a direct line of sight (LoS). Weapons fired in a parabolic arc are often the ones with minimums above 1.
Ranged Direct

Ranged Direct Eight

Ranged Direct Penetrate
This is a subset of Ranged Direct WATs that can damage multiple adjacent targets. Limited to four or eight directional attacks, these projectiles will continue going until they hit a wall or are blocked by a target.
Ranged Other
While most Ranged Direct WATs are restricted to four or eight directions, there are exceptions such as the Wand weapon type which fires a straight projectile, but can be fired directly in any direction, making every nearby tile a target. This type does not penetrate and will end if it hits a wall, the target, or any other interfering object.
Special
Lastly is the Special WAT. This is a rare type that is often assigned to specific weapons rather than entire Weapon Types, with some exception. For example, currently in planning is a Weapon Type called the Instrument. These weapons would actually target multiple tiles at once in a specific area. There may even be weapons that exist that can target every tile on the map!
Weapon Types
One Handed Melee
Axe
Mace
Dagger
Sword
Longsword
Foil
Sabre
Flail
Two Handed Melee
Staff
Fist
Tome
Whip
Polearm
Greataxe
Greatsword
One Handed Ranged
Crossbow
Pistol
Wand
Thrown
Two Handed Ranged
Bow
Greatbow