Effectively all of it is funded by the shareholders who "own" the corporation.
In the current example if the cash is coming from a debt instrument is it not bank funding it now?
it is typically about who is fronting the money now, it could be your bank making loans, or from cash reserves you have, fresh stock issue, selling another asset, or even the target's bank as in the case of LBO.
The shareholders always end up paying for it eventually in some form or other. Differentiating it by the current source helps understand the deal structure and risks better.
It's still the shareholders even if debt financing is used. The shareholders, through the company, have to pay off the debt. It increases the risk of bankruptcy.
When doing a deal, it comes down to price and source of funds. Changing either can drastically change how good or bad the deal is.
It's just different forms of shareholder assets being traded for other assets, by the shareholders (or rather, their majority vote).