Is it for fame? Nah - Diddy would have to shoot his girlfriend to get more press coverage than what he does now, word to OJ.
Is it for the "love of the game"? Nope - Jay-Z seemed happy enough making noise with his guest verses and throwing a farewell concert every 9 months.
Is it for money? Yes, but not in the direct way most people think. Making money off of CD sales is a loser's game, with a notoriously slim margin.
Instead I think Sean and Shawn are more concerned with with 100 million plus their respective clothing lines bring in. There are no official numbers for what Jay's Roc-a-Wear and Diddy's Sean John are worth, but a NY Post profile on Dame Dash from last year revealed that the apparel game is the real cash cow for The Roc, and beats the money from music times ten. The music they create serves more as marketing.
This strategy of back door earnings isn't the oldest, but it's definitely the smartest trick in the book. For instance, McDonalds doesn't make money on burgers and fries - they use the salty food to make you thirsty for their overpriced soda, which costs pennies to make. In the same way, U-Haul doesn't make money on truck rentals - the real business is overcharging for moving accessories. And auto makers will sell you a car for cheap - as long as they can trap with their expensive financing.
For my readers who study economics, you'll recognize what I'm saying as the "profit pool"of the hip-hop music industry. So, when you read about Jay's promotional world tour and Diddy's video blog, remember that what's at stake for them isn't the pitiful money they get from record sales, but the 3-figure millions their clothing lines bring in, which all rests on the lifestyle image they create for their companies, through their music.