A wallet is a hand-held pouch that you carry with you to hold your money and other personal items, such as credit and debit cards. A purse is a bag or case that can be carried over the shoulder or across the body.
A wallet is a small piece of cloth or leather, usually rectangular, and held in one hand with four or more card slots on one side and a pocket for coins on the other. It can also have additional pockets for change, receipts, business cards, etc.
A purse is typically an item of hand-held luggage designed to hold personal items such as cosmetics, money, keys, cell phone, etc., which is carried by a strap over one shoulder.