Why Would Someone Look at EV over EqV?

Is it correct to say that someone might look at EV because they want to acquire the operating assets of the entire company and see its value to all investors(like debt and preferred stock etc.)? Why would someone look at EqV over EV? Could a possible answer be that they plan to invest in the company but not buy the whole company or take a controlling interest?

I understand the concepts of EqV and EV, but I'm confused about when someone would want to look at one metric over another. Plus, it gets confusing with purchase price when people say EV is what you pay during an M & A deal, when in reality it's not. You usually pay the equity value plus some premium for synergies plus transaction fees right? Usually the acquirer refinances the debt or assumes it right? This doesn't affect the price to acquire the company, but I guess you could argue it affects the net transaction value.

Thanks for the help!