I am neither of these people but I do have an understanding of this! On a basic level: debt finance = you, as a company, are raising money by
borrowing (e.g. a loan, such as from a bank, a group of banks or credit fund). equity finance = you, as a company, are raising money by
issuing shares (aka equity) to either existing or new shareholders of the company (could be other companies or individuals acting as shareholders). These entities or individuals will pay you money for those shares. Very basic pros and cons: if you give equity in your company, that means you are relinquishing/diluting control of the company as equity in a company often gives you voting rights (or if not voting rights, economic rights). You may have a founder who owns 60% of the equity in the company who does not want to lose their controlling stake for example. You may not want to go for debt if interest rates are high, meaning the payments you make on the loan will be higher. If the company already is struggling slightly, further debt could bring in a risk of insolvency. Moreover, depending on the type of company you are, you might not be able to get a loan to begin with (if you're a really small company, the bank would want to secure it against the personal assets of the founders/owners) OR the loan you can get isn't large enough to cover the amount of capital you need to raise.
If you're concerned with debt finance (aka leverage) in a PE context, I suggest researching why leverage is so commonly used in this industry. The short answer is that it boosts returns far more than if you used equity (the committed capital in a PE fund) to finance acquisitions of targets. That's why you'll see ratios of like 70/30 or 60/40 debt to equity ratio. The return on equity is just SO much higher in PE if you use leverage. Part of this is tied to the fact that using debt (and some equity) to finance acquisitions means that a single PE fund can make far more investments using leverage than just using the committed capital of that fund. This is also a reason why PE can be controversial - the debt doesn't sit with the fund or the PE manager or GP - it sits with, you guessed it, the company that the PE firm bought and will eventually sell off, and partly because of this, not every company that gets bought by PE has a happy ending!
Hope that helps

Definitely more pros and cons than those listed but I wouldn't expect you to need to know more for interview.