In general, "cartera" is used to refer to any small, handheld bag that is used to carry money and other personal items. However, in some Spanish-speaking countries, such as Spain, "cartera" is more commonly used to refer to a wallet, while a purse is typically called a "bolso".

Generally we use "bolso" for a "handbag" - bolsa is used to refer to a plastic bag, a paper bag... (not a handbag) - although you may hear it in some parts of Latin America, (probably in Mexico) as handbag as well, but I don't think that is a very extended use.