If you dig into finance theory they're not as different as you might think. And it gets even fuzzier when you consider instruments like convertible bonds.
if they weren't different then why would the bond need to be converted from one to the other?
I wrote they weren't as different as you might think in terms of who has claims on the company etc. At the practical level there are obviously differences between different classes of stock, callable vs. not callable bonds, convertible bonds etc. I'm just saying that equity vs. debt is not binary.