If you go shopping for two different things you don't expect to pay the same price for them, right? Of course not. But why should the same amount of time spent with the same number of guests cost more if that event is a wedding? Because there's typically so much more work involved:
Weddings involve a number of events (usually at least three — the ceremony, the cocktail hour, and the reception) all taking place in one day, and they have to flow together seamlessly. There are logistics involved like moving guests from one venue to another, setting the room for one event then resetting it for the next, and making sure deliveries to multiple locations happen accurately and on time. Each of those wedding events also requires its own design work, which involves hours of research and planning. Birthdays typically involve one event: The birthday party, which happens in one location.
Wedding receptions feature a number of what I call subceremonies: Introductions, welcome address, dinner blessing, cake cutting, garter and bouquet tosses, first dances and other special dances, a choreographed exit, and often more. Birthdays involve some of these as well, but typically not as many. Plus, again, birthdays lack a wedding ceremony or anything similar. Making sure each of these subceremonies happens on time and smoothly requires a great deal of behind the scenes planning, plus coordination with the rest of the vendor team. The wedding planner, DJ, photographer, videographer, and catering staff all have to act in concert to be sure the events unfold as planned and are beautifully photographed and filmed, because there's no redo. This amounts to hours of additional planning work before the event even happens.