Can a star be massive enough to go 'supernova' yet not be massive enough to leave behind a neutron star? Or, perhaps vice versa? From what I understand, stars that explode as a supernova at the end of their lives become either a black hole or a neutron star, and less massive stars that do not explode become white dwarves, but...
Do those two mass limits overlap exactly?
This diagram from the Wikipedia article on supernovas mostly answers your question I think.

There is in fact an interval that is expected to not produce a remnant, but it is not at the lower end of the mass range, interestingly. Instead it's a result of the particular mechanism that triggers the supernova for these heavy stars, which blows the core apart entirely.