A "shower" is given for the bride before the wedding by the maid/matron of honor. It is a party that women attend and they bring gifts for the woman's household, etc. She is "showered" with gifts.
Similar showers are given before a woman's first baby is born. Then it's a "baby shower."
Wedding gifts are given by people who attend the wedding ceremony and/or reception.
Wedding shower gifts are usually more practical and less elaborate than actual wedding gifts.