.schem, .litematic, .schematic and .nbt
Four extensions turn up on schematic downloads. They are four different file formats from four different eras, and only one tool reads all of them.
.schematic — the original
The MCEdit format, from 2011. A flat NBT structure with a numeric block ID per position. It predates the flattening in Minecraft 1.13, so block states are stored as numbers that no longer mean anything to the modern game. Converters handle it, but detail is sometimes lost. WorldEdit and Schematica read it; Litematica does too.
.schem — the Sponge format
WorldEdit's modern format, built after the 1.13 flattening. Blocks are stored by their
real identifier (minecraft:oak_stairs[facing=east]) rather than a number, so
nothing is ambiguous. This is the format to prefer if you are using WorldEdit.
.litematic — Litematica's own
Litematica's native format. It stores multiple regions in one file, keeps entities and
block entities, and compresses well. It also stores the build's own metadata — author,
name, the region layout — which is why Litematica shows more information for a
.litematic than for the others. Only Litematica reads it.
.nbt — structure blocks
Minecraft's own structure format, written by the structure block and used by data packs. Size is capped at 48×48×48, so you will only see it for small builds. The game itself reads it, which makes it the right choice for anything going into a data pack.
Which to download
If you have Litematica, take whatever is offered — it reads all four. If you are pasting
with WorldEdit, take .schem. If a build is only available as
.litematic and you need it in WorldEdit, convert it first; the
editor here loads a .litematic and can save it back out
in another format.