My understanding is that the primegen application generates lists of sequential prime numbers. The goal is to build a comprehensive list of prime numbers from the smallest number on up. The lists are available as DVD ISO images downloaded via torrent.
By contrast, the LLR-based searches (Twin Prime, Cullen, and Woodall searches) attempt to find primes of a specific mathematical form. These primes are much much larger than those generated by primegen, enough to break world records of the largest primes of their respective forms.