What do you call someone who either borrows money, or receives equity funding?

As someone involved in the venture-capital space, I would use different words depending on the scenario in question.

• Someone who receives money in exchange for a promise to pay it back later is called a borrower¹, and the person making the loan is the lender:

A person that has applied, met specific requirements, and received a monetary loan from a lender.

• Someone who receives money in exchange for equity is called an investee¹, and the person investing the money is called an investor.

A company or entity in which an investor makes a direct investment.

• You could also use investor to describe a person who loans money, in the case of a loan. But I would probably always call the recipient a borrower, not an investee: the goal of the investment is very different in the two cases.

¹Investorwords.

The receiving end of the arrangement would be the "investee". From www.investorwords.com:

A company or entity in which an investor makes a direct investment