According to IFRS What is the difference between Equity method &costing method when a holding company record it's investment in a relative company

The question is vague and incomplete as the scope of the question is very vast It depends if the investment is on subsidiary or associates, or it is when preparing a standalone financial and consolidated one.
In consolidated balance sheet the carrying amount of parent’s investment in subsidiary will be eliminated against parent’s portion of equity in the subsidiary will be eliminated.
It is only when a parent company prepare a separate financials, the investment in subsidiary will record on the cost method or based on IAS39 where investment will be recorded either under ‘available for sale investments’ or ‘investment carried at fair value trough profit or loss’ The investment in associate should be recorded based on equity method, where the investment will initially recorded at cost and subsequently the carrying value will increase or decrees depends on the share of profit from the investee.
The share of profit distribution, if any will bring back the investment in investor’s book to the original level.