You may have heard or read something about both of these terms related to Foreclosure. These terms are distinct and mean different things.
For example the reinstatement period is the time referred to in the Notice of Default during which the borrower/seller can make up their missed payments and late fees to bring their account current. Doing so stops the foreclosure process. The time period is state specific. Check with your lender to know how this might apply to you.
On the other hand, the redemption period is a period of time after the foreclosure that allows the owner to redeem the property. The owner would pay the sale price, interest and any other expenses.
TEXAS HAS NO REDEMPTION PERIOD.