Yes, usually they are seperate and different groups of people are invited. A bridal shower is for (primarily) women of all ages - mom, grandma, aunts, sisters, friends, etc. Gifts are brought, sometimes fingerfoods or snacks are served, and occasionally games like "toilet paper wedding dress" are played. A bachelorette party is usually just younger women. They often go to a club or have a small party at someone's house and sometimes naughty/fun gifts are given - lingerie, sex books, massage oils, etc. The bridal shower is usually hosted by a friend of the family or extended family member or even a bridesmaid, while the bachelorette party is usually hosted/put together by the maid of honor.
at 8:43 AM on Jul. 12, 2008