Difference between Sculpt and Mesh

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Sculpted prims are prims that get their shape based on a texture file. This colorful texture, also called a Sculpt Texture or Sculpt Map is a standard texture where the R (red), G (green) and B (blue) channels are mapped onto X, Y and Z coordinates. The sculpt map is build up of 32 x 32 faces which give us a total of 1024 faces. Read more on the page ‘Understanding the sculpt map format‘ from Domino Designs sculpt_map_uv_layout

More detailed and technical information you can get by watching this very good video from Machinamatrix. Note that this video was made in 2011, that is before the word mesh was introduced in Second Life. If Gaia in this video talks about meshes, she means sculpted prims, not the mesh as we now know that is used for avatars and clothing

New Mesh is a more complex build. Where a sculpt cannot use more than the fixed 2000 triangles, the new mesh can have all kind of topology.Triangles You can punch a hole in a mesh object and shape it any way you want while creating it. While a sculpt is imported in Second Life using the sculpt texture, the mesh is being uploaded as a Collada file (.dae or .xml files). Read more about mesh on this very informative page of Machinamatrix.

I have tried to make a (far from complete) list of features to illustrate the differences:

Sculpty   New Mesh
Upload costs 10 Lindens depending on the model’s complexity
Land Impact (formally only known as print count) 1 independent of the size depending on the model’s size and complexity
Flexibility non what so every – stiff can be rigged which means it can be connected to the skeleton bones; if the bones move, the mesh moves with them. Thus it becomes movable, although not flexible.
Texturing one texture face per prim can contain up to 8 texture faces per prim
re-sizing in world can be freely resized up to 64×64 prims NON rigged mesh can be resized up to 64×64 meter, but this will increase the land impact (Li) dramatically.
Rigged and fitted mesh cannot simply be resized since the build is connected to the bones. The mesh WILL resize if you change your certain parameters of your shape.