Bank

In the old west banks were primarily used to safekeep the Settlements' riches, Becauce of the amount of gold and Money stored in a Bank it was often the prey of Outlaws

Banks
In Red Dead Redemption banks are confirmed to be in the singleplayer, However what their current use is is still unknown.

However it has been confirmed that the player may get a random generated side-mission/Job when walking around town to retrieve The banks' safe which then has to be brought back to Bank.