Working for your self in my own understanding simply means running your own personal business, not working under any firm or any company own by someone else but you are running your own personal business.
Agreed. You can't say you're self-employed when someone else is paying your salary. Working for yourself is self explanatory because it's when you aren't the owner of the business then you're working for someone. Even when that someone is family or friend. Unless you're part of the company that you and your friend or family joined resources together to open then that's when you can say you're working for yourself. There are two ways of working for yourself and the first is doing everything alone while the second is having a partnership. Not everybody can own a business and not everybody is supposed to be working for others.