So far, from what I could read online (in this guide and on the wikia, among other sources):
Briefing screen
Pay grade
The pay grade for a mission indicates how much cash players can expect to get out of a mission -- source.
Also this thread suggests it can go up to 10 stars.
Day rate
The dayly income rate is a cash reward with a multiplier for the day a heist takes (e.g. 1x in The Bank Heists and 3x in the Rats Heist) -- source.
Contract pay
The contract payment is a flat amount of cash reward based on the number of white stars (pay grade) -- source.
Payday
The overall payday is the sum of the other two cash rewards (pay grade and contract pay) and will be shown on the map if you select a heist -- source.
Yellow bonuses
These bonuses come directly from the difficulty (or "risk") of the mission, pictured by the yellow skulls on this very same screen. Normal = no skull -- overkill = 3 skulls.
Debriefing screen
Instant cash and bag loot items
The instant cash it the one you loot and put in your pockets directly during the game (jewels, cash bundles, ...) The bags are those heavy packs of money, jewels or even drug you'll have to carry in order to achieve a mission.
Balance
This section contains the sum of all the amounts contained in the Income section ($332,400 in the example given in the question) distributed between two type of accounts: the offshore account and the spending cash.
Offshore account
The offshore account consist of most of the money players steal during the course of their heisting career.
The player has no way of interacting with their offshore account and is only used to show off how much the player has stolen -- source.
Since August 30 2013, you can use your offshore account to directly buy specific missions from Crime.net.
Spending cash
The cash you get, finally. In the given example, it's 10% of the total amount, but so far I couldn't find any precise calculation to know if that percentage can vary or not.
This is the offshore account money and 10% of that becomes you spendable cash. -- source.
Best Answer
It takes just under 90 seconds for the money to burn. This time appears to be the same across difficulties and Regular/Pro. As you can see in the screenshots below (taken immediately after the money was ignited and immediately after the camera became available for pickup on hard and overkill difficulties respectively) the duration is about 88 to 89 seconds in both cases.
Start (Hard Difficulty) - 9:21
End (Hard Difficulty) - 10:49
Start (Overkill Difficulty) - 7:07
End (Overkill Difficulty) - 8:36
It's possible that (like so many other things in Payday 2) the duration is based on a random number generator and I just happened to have two of the same durations, but for now I'd say that the duration is most likely just under 90 seconds.
Update: I just timed the burning duration on Overkill (again) as well as Pro Hard, and both were almost exactly 90 seconds.