How does corporation tax work in practice?
A sole trader pays income tax on profits through Self Assessment. A limited company pays corporation tax instead, on its own profits, as a separate legal person. The director then pays personal tax on whatever they take out as salary or dividends.
The company is responsible for calculating its own bill. Nobody sends one. Profit from the accounts is adjusted for things tax treats differently, such as depreciation being replaced by capital allowances, and the rate on gov.uk is applied to the result.
The rate and any small profits relief change at Budgets, so the figure to use is always the current one on gov.uk. The mechanics do not change: profit, adjustments, rate, pay, file.