David, it could be for a number of reasons, lens choice is only one of them. In addition to camera equipment or settings, it could have to do with the light conditions or the moon phases or the weather.
Here's a blog post I made a few years about tools for planning Milky Way photography--you might find it helpful: Tools for Planning Milky Way Photography - NikonForums.com
If you want to share some of your attempts and tell us when you were shooting and what your settings were, we could possibly help you figure it out.
Edited to add, that no, it's not going to be as easy to capture the Milky Way with your kit lens (18-55). I'm not going to say it's impossible because, honestly, I've never actually tried it with a kit lens. Your aperture on that lens is more limited, so that will influence your exposure. You can get a fairly inexpensive wide angle lens that will allow you to get these types of images--for instance, you may want to check out the Rokinon/Samyang/Bower 14mm 2.8, which can be had for a few hundred dollars. I use one often for Milky Way photos and get pretty good results.