Underwriter = just loads money into the club (one lump sum normally)
Background = money pumped in only when needed
Foreground = is actively involved pumps money in monthly
I think to be more technical an underwriter underwrites your debts and just spends what is needed to keep you going and background and foreground should both put cash in, but more coming from foreground.
Underwriter: Clears debts, doesnt put anything additional in.
Background: Puts some money in but not huge amounts.
Foreground: Pumps in money left right and centre a la Man City