If you have started working for yourself. You are not working in partnership with anyone else and you are not operating as a limited company. You will be classed as a sole trader.
Anyone who operates as a limited company. Even if you are the only person involved in the company. You will not be considered self employed by HMRC. You are considered an owner and possibly an employee of the company. However, owners of a limited company may still have to register for self-assessment.
Partners in a partnership will individually be considered self-employed. However, they will not be sole traders. The partnership they operate will also be registered separately with HMRC.