MDF stands for Medium Density Fiberboard. There is an excellent website which describes this material at http://www.nelson-pine.co.nz/nels003.htm. Be sure you wear a respirator or at least a dust mask when you cut either of these products. You already know the reason on the particle board, but with MDF, the airborne dust particles will play HELL with your sinuses. MDF is used just about anywhere you see white painted millwork in a new home, usually as baseboard and other trim. MDF also finds its way into various furnitures, shelvings, etc. It is desirable because its fibers are much smaller, the edge and surface profiles are much truer, straighter, cleaner than particle board. DO NOT get it wet under ANY circumstances, or it will swell up like a balloon!
MDF does not have the same formalahyde issues that particle board does, and any off gassing that it might do would usually be offset by the fact that in most applications, you will be sealing it with a paint finish of some type.
MDF is not a structual material, but works very well for the applications I described above.