Ammonification is conversion of peptides, amino acids, and nucleic acids into ammonia in the form of NH3. It's done by microorganisms such as Bacillus spp., Proteus spp., and Pseudomonas spp. and usually takes place in soil. It can be either an oxidative or reductive process.
Nitrification is the conversion of ammonia in the form of NH4- to NO3- through a two-stage process both involving the addition of oxygen (oxidation).