Finance tends to be specific for one thing - you get finance to purchase a car or a house etc. and the agreement is specific to that item.
For instance if you take out finance on a car - if you stop paying, they will come and take the car back.
A Bank loan is usually for any purpose and you can spend it on what you want, how you want. If you default, they'll take you to court etc. but they can't take away what you purchased with the money as it's yours to do with what you wish.