The loan agreement lists the terms under which a loan is given. The bank is the lender, and any borrowing entity--individual, partnership, company--is the borrower. The loan agreement covers many of the same terms and conditions as a promissory note, although it is longer and more complicated.
The subsidiaries remain private. They are private subsidiaries of a public company. Think about it: if a subsidiary went public, that would mean that its shares were being offered to the public, instead of all being owned by the parent company, and so it would no longer be a subsidiary.
This means that, in most cases, the company is owned by the company's founders, management or a group of private investors. A public company, on the other hand, is a company that has sold all or a portion of itself to the public via an initial public offering (IPO), meaning shareholders have claim to part of the company's assets and profits. One of the biggest differences between the two types of companies deals with public disclosure.