Same as File ‣ Link…

The asset will be linked to the current blend-file, and thus be read-only. Later changes to the asset file will be reflected in all files that link it in.

Same as File ‣ Append…

All of the asset and all its dependencies will be appended to the current file. Dragging a material into the scene three times will result in three independent copies. Dragging an object into the scene three times will also result in three independent copies.

“Dependencies” in this case means everything the asset refers to. For an object, this can be its mesh and materials, but also other objects used by modifiers, constraints, or drivers.

Since the file now has its own copy of the asset, later changes to the asset file will not be reflected in the file it’s appended to.

Specific to the Asset Browser.

The first time an asset is used, it will be appended, including its dependencies, just like described previously. However, Blender will keep track of where it originated, and the next time the asset is used, as much data as possible will be reused. Dragging a material into the scene three times will only load it once, and just assign the same material three times. Dragging an object into the scene three times will create three copies of the object, but all copies will share their mesh data, materials, etc.

Since the file now has its own copy of the asset, later changes to the asset file will not be reflected in the file it’s appended to.