Differences from Minecraft

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Minetest

Minetest is a work-in-progress, there is still much work ahead
World size is ca. 60000 blocks in all dimensions (including height)
Built-in modding capability based on Lua (considered one of the core features of Minetest)
Mods work server-side, you can join any random server and it will work out of the box, no matter what amount of crazy mods the server is using
Crafting recipes are not automaticlly mirrored unless there's an explicit recipe definition for it
Smelting time of items can differ on a per-item basis
No dual wielding
Built-in minimap and radar (press F7 to view)

Torches can be attached to the ceiling
Water does not make other blocks like torches drop (but it can destroy Snow)
Dropped item stacks must be leftclicked to be collected, the player is not a magnet ;-)
When mining, items directly go into the player's inventory, unless the inventory is full
Hoes can be used on Desert Sand
Wheat and Cotton don't grow at all when the soil is dry (→Soil, Desert Sand Soil)
When a player dies, Bones are created and all items are stored inside
Some tools or items are used on left click instead of right click (for example: Bread)
The Sneak Glitch
Water and liquids in general don't slow down the player as much when falling into it

The crafting grid acts like an inventory; the items don't drop when you close your inventory
No crafting table
Players have a 3×3 crafting grid in their inventory at all times
The furnace has 4 output slots instead of 1
Very different burning and smelting times, see Smelting

Water and Lava have a flowing distance of 8 blocks
Some blocks can be owned by players: Locked Chest, Steel Door, Steel Trapdoor; with Skeleton Keys player can share access.

Redstone mechanisms: Mesecons (Mese is then considered to be the redstone equivalent)
(There are many more mods, someone should write it down here)