What is a play date?

Are 4 year olds really supposed to know how to entertain and enjoy each other? I'm getting lots of requests to arrange play dates with school friends, and I find my reluctance just keeps growing. Then last night, E's pal's dad called to ask her to come for a play date today. We had made plans to go to the zoo in the morning, so I arranged a visit to start at 4pm. Maybe that was my big mistake. Anyway, it wasn't a big success. I don't think it was terrible, and E would still like her friend to come to her house, but they never got into a rhythm and managed to play together. And when I think about it, I don't know that E ever manages to play with other kids very well. She likes to do her own thing. She plays pretty well with her sister, but usually she wants to do what she wants, and she is unyielding. Is it just her, or is this typical. I felt like the friend was more experienced with the set up (as an only child) but when we arrived, he wasn't ready to be very social or even talk to E.