Rarity

Rarity and Quality are properties of Items, which are represented in-game by the color and name under the item's name and (in most cases) by a title prefixed to the item's name. An item can have only one rarity and quality, which is determined when the item is created and remains unchanged, except in rare circumstances.

Rarity and Quality are purely cosmetic properties, and have no effect on gameplay other than some additional on-screen messages.

Strange
Strange is a quality introduced with the Dota 2 Store. Strange items are virtually all items that are obtained commonly from opening Treasure Chests. All Strange items have the capability of upgrading the rank prefix on their name, based on tracking a count of a specific in-game event, usually the number of players that the weapon has killed.

Rarity
Items with a higher rarity have a less drop rate, than items with a lower rarity. There are currently five rarities in use, which names are as follow: Common, Uncommon, Rare, Mythical and Legendary (Ordered by it's rarity).