Is there suppose to be separate wedding and bridal shower gifts?
A wedding shower is a modern social contrivance. Whether you subscribe to it or not is up to you. Wedding showers were instituted to help equip couples who were starting their first household together. Nowadays, when many couples have either lived together or lived on their own prior to marriage, wedding showers are more often used to upgrade what the couples already have or for the couples to obtain luxury items for their households. There are even couples, that etiquette considers greedy, who request cash only gifts for showers and/or weddings that they want to use for their honeymoon, house downpayment, or other expense.
