A wallet is usually just for paper money, and doesn't have a pouch for coins. My wallet actually has a tiny change purse as part of it, but that's pretty unusual--I had to hunt a ton to find one that had space for coins, bills and credit cards and wasn't as big as an airplane.
So bottom line:
Wallet if it's mainly for holding paper money and credit cards. Some wallets have pouches for coins and can still be called wallets. Change purse if its main function is to hold coins and maybe receipts, phone numbers etc.
Many women here have wallets with a purse combined. This holds a reasonable amount of change in a zipped central part, credit cards and such on either side of the purse area, bank notes, receipts and so on in a pocket right across the back of it. Mine is 10cms x 8cms x 4cms, or 3ins x 4ins x 1.5ins, so it's fairly bulky I suppose. We just call this a purse and we keep it in our (hand)bag.