Model

Models are 3D meshes used for Quake's player, monsters, weapons, and power ups that use the mdl file format. The rest of the ammo, health, and exploding boxes use the Quake BSP Format. The original mdl models were created for Quake in Alias PowerAnimator. They are sometimes referred to as "Alias Models" which is derived from the program's name. The textures for the models were orignally created in [Deluxe Paint|http://en.wikipedia.org/wiki/Deluxe_Paint].

MDL

Models are 3d meshes made up of triangles. They use an 8-bit indexed texture with the Quake palette.

BSP

BSP models are very same type that make up the maps in Quake, but on a much smaller scale.

Sources

http://forums.insideqc.com/viewtopic.php?f=13&t=5676
http://www.gamers.org/dEngine/quake/QDP/makemodels.html
http://www.gamers.org/dEngine/quake/spec/quake-spec34/qkspec_5.htm
http://www.insideqc.com/qip/q1/qfix.htm
https://en.wikipedia.org/wiki/Binary_space_partitioning