How does rewarded money work (pay grade, day rate, offshore account, ...)?

How does rewarded money work (pay grade, day rate, offshore account, ...)?

I'm having a hard time understanding how money works in Payday 2, it was
way more simple in the first opus.
In a mission's preview, you can find different amounts of money:
pay grade (which seems to be some sort of gauge)
day rate
contract pay
something that looks like potential bonuses (in yellow, on the right side
of the amounts)
the payday which looks like the total of all that

Once the mission is complete, you get a debriefing screen with two sections:

The day rate and contract pay don't differ from the first screen, even if
I have no idea of what it is exactly. Then there are the bag loot items
(if looted all the bags during the mission) and more
I-have-no-idea-what-it-is stuff like the instant cash, the offshore
account.
And, finally, the only amount that is revelant to me, the spending cash
(in green) which is what you actually get in your wallet after the
mission.
In addition to all that, my friend and I are receiving different rewards
at the end of each mission (I always receive a few thousands more than he
does): we checked and we don't have skills that impact missions rewards...
I just have a few more levels.
Sooooo... Any idea what are all these stuff and how the final instant cash
is calculated ?