Offline players will earn more credits than online players during campaign, firefight, custom games, and forge. However, offline players should have a daily maximum cap of how many credits they earn. Online players have no credit limit (or is too high to be achieved legitimately)
Also and most importantly, if an offline players decides they want to go show off all their armor online, then well there is this...
If you initially earn offline Credits and then take your profile online, there will be a onetime check to see how many Credits you’ve acquired. If that amount is over 26,250, you will need to forfeit some Credits. This check is in place to ensure a level playing field and to eliminate foul play.
If you choose not to authenticate, you can still play online, but you will subsequently appear as a default Spartan with a default emblem and colors. If you want to change your mind, simply reboot your console and upon your next foray into online matchmaking, you'll be prompted again.
If you have purchased shiny new Armory items, the authentication process may reclaim armor pieces in order to bring the Credits balance into a positive state. The end result is Armor + Credits = 26,250. No more, no less.
If you have less than 26,250 lifetime Credits earned when you go online for the first time, you won’t have to worry about any of this complicated math.