I'm sorry if my English is not perfect.
The main characteristic of the Great Depression was the lack of faith in the bank system by the citizens, who made lots of banks go bankrupt because all their reserves were demanded by the public. You should know that a bank doesn't have all their deposit in liquid assets so, the panic of loosing their deposit made the public run to the banks to withdraw their deposit before the banks had no money left.
The main characteristic of the Stagflaction was the increase of prices correlated with a decrease in the demand because of lost of business tissue. The oil prices skyrocket during the crisis and the increase of prices led to a scarce demand what surely cause a new increase of prices.
The main characteristic of the Great Recession was the spread bankrupt of banks dedicated to buy morgages. This "trash mortgages" (like they are called in Spain) were divided in parts and sold globally. As this mortgages were unpaid because the agreements were too soft for the borrower, banks had to improve their balances so the most liquid asset (stocks) were sold at the same time collapsing the stockmarket and making even deeper the losses. These losses led to a credit crunch (the lack of credit in the productive economy) spreading the crisis into the productive economy.
I hope it's helpful!