Titles are just that, titles. They mean nothing to your actual ability, you can give your janitor the title of CEO but he is still a janitor. I always figure that a sole proprietor who needs to call himself a CEO is compensating for other shortcomings they might have. A CEO, as it is normally defined, can only exist in the context of the board of directors. If you dont have a board you aren't really a CEO, you are an owner. But you can title yourself anything you want to.

A sole proprietorship is more of a tax provision and freedom than a form of business. Any citizen can at any time choose to do business under their own name, no paperwork or anything like that is required. Since it is a single member you are whatever title you give yourself. The downsides are that you can not operate a real business name and you have unlimited personal liability for what happens. Understand that personal liability means that you can loose anything you own as payment if someone is aware money in a lawsuit. Other forms of business allow for insurance and other provisions that make this impossible. This is not a good form of business to use.

Single member LLCs or corporations (like what I run) are often regarded as sole proprietorships and we can select to be taxed as one as well. That may have been what he was referring to. In either case that option seems to indicate he wants you to work on your own or he himself did not understand what the option means.

It seems that he is giving you three options:

1. Work for his business.
2. Run the business with him
3. Run the business

Each comes with its ups and downs, as you gain power you also gain responsibility and liability. If you are in a partnership you cant just say "pay me" even when the business is going bad, if you don't carry proper insurance you can also be liable for anything he does in the business (and vice versa).

Here is what I would recommend for each option:

1. Come to the US and do what he says, it isn't your company.

2. Get familiar with US law and read a few books specifically on the subject of contracts because you are going to want to understand the one you will be asked to sign (or will insist he signs). Do not enter a partnership without a contract, I've had two law teachers say that doing so is the fastest known way to court.

3. Get familiar with US law and read a few books about starting a US business especially until you understand how the tax process works. Do not just start a sole proprietorship, its just a bad idea.