Equity investment refers to investing in stocks of companies that are traded on a stock exchange. By investing in stocks.
A Mutual Fund is a "mutual" meaning shared, "fund" implies corpus.It is a facility whereby an investment company accepts investor's funds for investing into a pre-determined investment avenue.
Tax planning implies planning your financial investments and expenses in a prudent manner so that one can avail the maximum tax benefits provided by the authorities.
Planning your finances (expenditure and savings) in order to achieve particular financial goals is called financial planning.