EULA is meant to cover a software application; Terms of Service govern a website (including mobile Web) and underlying services. Either can be binding in "click-wrap" or "browse-wrap" form under US law. Both apply to every end user. The EULA applies to anyone who downloads and uses the software. Unless otherwise specified, TOS applies to everyone visiting the site, which often contains both public and private areas. In neither case are they necessarily registered or paying customers.
The second part of this question is specific to enterprise licensing. Again using Dropbox as an example, you can read and download its separate TOS for a Business account. In theory, at least under US law, virtually all terms and contracts could be approved using "click-wrap" agreements. In practice, while small business agreements are often done with an online click-through, larger enterprise deals are far more likely to be documented by a comprehensive license/services agreement. (This may be in addition to, not instead of, the EULA or TOS.) That agreement requires signature by a person with authority to enter into contracts on behalf of the customer business entity (corporation, etc.).
Disclaimer: I'm a California licensed attorney, but this is legal information, not advice. Laws can vary dramatically between jurisdictions.