Difference between fuse diode and diode - is there is any?

I have a BSA motorcycle with a couple of lucas 1 and 2 amp diodes in the electrics. It is hard to find the original 2 amp lucas diodes so I am thinking of using a standard 2 amp fuse diode instead. What is the difference between a diode and a fuse diode. I am thinking a fuse diode fails safely if overloaded with current whereas with an ordinary diode the whole circuit will get hot and possibly burn out the wire in any random place. Or is there no difference between the two.