The charge is what they require you to pay, and the price is what you pay. The shopkeeper 'makes a charge' (or 'charges [v] a price', or just 'charges'), and the customer 'pays the price'.
PS My definition is mainly of the nouns, although I mentioned the verb 'charge'. The shopkeeper also 'prices': He bought a box of 12 for £5.00, but priced them at £1.00 each - making a whopping profit of over 50%. . The verb 'price' is often seen as a participle: 'priced at' means 'with the price set at'.