Where do you see the terms "stock basis" and "tax basis"? Those are not common terms in relation to income tax. The usual term is just basis. You will also see "cost or other basis," which often gets shortened, somewhat illogically, to "cost basis."
Basis is your cost for acquiring an investment or other asset. If you purchased the asset, your basis is the amount that you paid for it. When you sell the asset the difference between the amount that you sell it for and your basis determines your gain (profit) or loss. You report the selling price and the basis on your tax return for the year that you sell the asset. Other than that there is no reporting of any kind of basis, at least as far as income tax is concerned.