I recently had an external hot water tank attached to my tankless oil burner furnance. I want to know if the thermostat setting on the furnance and the thermostat setting in the external tank should be the same.
Also, I would like a brief explaination as to how my setup works.
I was told that when hot water is used it comes directly from the external tank. And that hot water is fed from the water tank in the furnance into the external storage unit when needed. When does this happen?

The boiler water heats the water in the indirect tank on demand of the tank thermostat (like another zone calling for heat) until the water is heated to what you want to set it at for your preferences. There is no government-mandated temperature the tank must be set at, short of blaming someone for getting scalded on that occasion.

The boiler gets as hot as it can to shorten the time it takes to heat the water, as heating water to 140F say with 140F water takes a LOT of time. So the boiler will probably get as hot as it can while being asked to heat the water by the tank thermostat. Thus you get information on the paper that comes with the tank in the box from the supplier to tell you things like to expect 100 gallons of water to be heated by a boiler with such and such an input at a boiler temperature of say 170F.

See page 3 here:
http://www.amtrol.com/pdf/BoilermateMC10009low.pdf

www.heatpro.us energy businessmen's knowledge

Yes, you really have to find out the MAKE and MODEL to get good answers. There IS more than one machine made.