They are similar but heating oil is thicker and a little bit harder to ignite. It'd probably be best if you found some way to clean out whatever dregs of heating oil remained in the tank. Adding biodiesel to the tank might help as it is a better solvent for "oil goo" than regular diesel fuel. You don't need to get the inside of the tank spotless, but if there's several unused gallons of heating oil in the tank you might have problems due to it raising the flash point of the diesel.

-Blast