All three terms describe the same thing: the amount left after every cost, including interest and tax, has been taken off revenue. “Net profit” is standard in UK accounts, while “net income” and “net earnings” are more typical of US reporting and financial commentary. They are not different measures.
You will also come across “the bottom line” and, in listed-company reporting, “earnings” used as shorthand for the same figure. Earnings per share, for instance, is built from net earnings divided by the number of shares in issue.
The risk is not that the terms differ but that the basis does. Before-tax and after-tax figures, or figures that include or exclude exceptional items, can all be described using any of these labels. Always check what has been deducted before you compare two numbers or use one in a calculation.
Set against these, EBITDA is genuinely a different measure — it deliberately strips out interest, tax, depreciation and amortisation, so it is never interchangeable with net profit. For confirmation of what any specific figure in your accounts represents, speak to your accountant. This is general information rather than accounting advice.