A drop is any item obtained from the environment, such as an item looted or "dropped" off of enemy mobs or found in chests. A drop is also known as loot.
Quest drop[]
A drop of a quest item. Many quest items only drop if the player currently has the associated quest in their Quest Log.
Most items that require a drop of only a single item, such as the retrieval of a specific item, or the removal of a head from a named mob, each player in the group that loots the mob can each loot one of the items.
Quest items that require you to collect a certain number of items can only be looted by one player at a time.
The former can be looted by any questholders regardless of loot priority (such as Group Loot or Free For All), the latter are looted as normal. If only one person has the quest to collect a number of items, they may loot from each mob that drops a quest item, regardless of loot priority. They will also be able to loot any money, and start any loot threshold rolling on items whose quality is at or above the loot threshold.
There are still other quest items that drop regardless of having the quest or not. Some of these have alternate uses, others are used only for the quest they are attached to. Often they are not soulbound items, and can be traded, sold or bought by and from players.
The final Quest Drop is the drop of an item that starts a quest. Each player in the group can loot the item, regardless of loot priority. The quest item may still have a level requirement, and some quest items of this nature can be used in other ways (e.g., Ghosthowl's Pelt may be used as a cloak).
World drop[]
A world drop is a (usually bind on equip) item that has a very low chance to drop from mobs, chests, or other sources within a certain level range. Some will only drop from specific types of creatures. World drops are largely impossible to farm for because none of their sources have more than a miniscule chance of dropping them. Because of their rarity, many world drops fetch high prices on the auction house—especially those with desirable appearances.
Some world drops have been affected by the various changes to zones' levels over the years. For example, [Oozing Bag]s drop from level 40+ oozes and worms in old world zones; but as of patch 9.0.1, mobs in these areas only scale up to level 30 unless you're on the relevant Timewalking Campaign.
Continent drop[]
This isn't a very widely used term, but some uncommon or better random drops are actually restricted by continent.
For example, items from the Bristlebark collection ( [Bristlebark Boots], [Bristlebark Bindings], etc.) can drop from any mob within a certain level range in Kalimdor. On the other hand, Silver-thread collection items (like [Silver-Thread Gloves]) only drop in the Eastern Kingdoms.
Zone drop[]
Zone drops are like partial world drops. They have a very low chance to drop from mobs within a specific zone, instance, or area. Like world drops, some of them drop from certain types of creatures—such as the [Crimson Dredwing Pup], which can drop from any dredbat in Revendreth.
Static drop[]
A drop that only comes from a specific mob or group of mobs.
Example: The [Spellforce Rod] only drops from Venture Co. Surveyors in a certain area of Stranglethorn Vale.
Boss drop[]
A type of static drop that only comes from a boss mob in an instance. The best ones are usually Bind on Pickup.
Epic drop[]
A drop of an epic quality purple item inside or outside an instance. Most drop inside instances, but there are a few that drop outside.
Legendary drop[]
A drop of a legendary quality orange item inside or outside an instance. Most drop from the highest level raid instance bosses and then only occasionally. In the Broken Isles, legendary items drop from dungeons, raids, and world bosses.
Artifact drop[]
A drop of an artifact quality (brown goldish) item. With the introduction of Legion, many artifact items are now dropped during class-specific questlines and from bosses.