What is the actual difference?
As a sole trader, you and the business are the same legal person. The money is yours, the contracts are yours, and so are the debts. You register for Self Assessment and pay income tax and National Insurance on your profits.
A limited company is a separate legal person that you own shares in and usually direct. It owns its money and signs its own contracts. It pays corporation tax on its profits, and you pay personal tax on whatever you take out as salary or dividends. That separation is the whole point, and it is also the source of every extra obligation that follows.