Old GM (formerly General Motors Corporation, now Motors Liquidation Company) got $19.4 Billion from the government.
It will be paid back through asset liquidation, possibly not fully, I don't really know.
New GM (General Motors Company) got $30 Billion from the government.
$6.7 Billion as a loan, which with this payment will be $2 Billion paid back.
So $4.7 Billion remains, which they will pay back as fast as possible... I'm sure they would love to do so before the IPO.
The other $23.3 Billion is the 61% ownership of GM.
When GM does their IPO, the UAW and Government ownership will be converted into shares.
The Government will likely sell most or all of their shares after several months, and will probably turn a profit on the whole deal. UAW will likely sell a majority of theirs as well.
Thusly, GM will again be a public company as before.
And after buying back the stock from the government and UAW, GM will likely spend most or all of the money raised through the IPO.
At least that's how I understand this whole thing.