I don't think it's currently correct (there's a base unit, but I don't know if it's that's hard limit or if it can be changed in future versions), but the difference is that when the government prints money, they get the money. The government printing money would be like someone issuing more bitcoins that don't already belong to anyone. Splitting up bitcoins doesn't change the fraction of all bitcoins that each person owns.

Plus, they're already "split up" as it were, it's just they're not valuable enough that people are using nanobitcoins or anything like that. It's only when the value of the currency goes up that people will do transactions in smaller fractions of a bitcoin.

Is that so? It sound more analogous to adding a 1/2th penny

You don't get more pizza when you slice it in smaller pieces.