Earnings before interest and tax (EBIT) is very closely related to operating profit and often the same. It may include some profits or losses that are excluded from operating profit.
EBIT is used in similar ways to other profit measures such as EBITDA. The valuation ratio that most commonly uses EBIT is EV/EBIT which is similar to EV/EBITDA - apart from the inclusion of depreciation and amortisation as costs. EBITA and EBITDA are generally preferable to EBIT, especially when used as a denominator for EV.
Trading profit is similar to operating profit and EBIT but excludes items that although do not arise from the regular trading actives of a business - certain asset sales for example.