From a practical perspective the difference is that with equity you accept a lower floor (you might get nothing) in exchange for a higher ceiling (your invest might 100x if the company goes public). That's the deal these investors signed up for and unfortunately for them they got option number 1. They're not owed anything because that's the deal they agreed to.
Additionally, my first point was one of metaphorical (social) debt.
Given the context and the fact I'm typing in English it ought to have been clear I was referring to the definition of debt in English. If that wasn't clear, I apologise for the confusion.
Only definition that matters is the one in the jurisdiction this startup was in.
This is incorrect. Please see the differences between equity and debt. [1]
[1] http://smallbusiness.findlaw.com/business-finances/debt-vs-e...
Firstly, to say there's no debt, monetary or otherwise, to someone who believed in your company enough to hand over their own money (or money in their control) to back you is just pure arrogance.
Secondly, there absolutely is debt. When a company goes into administration the assets are sold to pay out those who hold equity in the company. They're literally owed debt.
EDIT: To clarify for those responding saying that equity does not constitute debt...
Creditors and investors are different, absolutely. It is also correct that investors are typically paid last during administration (although investors may form agreements to come before other investors). Nonetheless, during administration, the administrator determines how much money the investors are "owed", which is literally the definition of debt.