That's right, there are different styles of wedding photography. Some wedding photographers will shoot in only one style, but a good photographer will help you find out what style you like, and work to tailor your photography to your preferences. This is your wedding day, not the photographer's, and you should be getting the photography you want, and not simply what someone thinks you might want. Here are some of the types of wedding photography styles and what they mean:
Contemporary wedding photography: This photography style is a relaxed informal way of capturing the day. But also bringing some of the more traditionally posed shots and making them more spontaneous.
Reportage or Documentary style photography: Documentary style photography is a normally a hands-off approach, the photographer is there to capture/document what is happening during the wedding day, without actually implementing any poses or set ups, so that the images tell the story of the wedding day with many very natural, candid shots (not looking into the camera)

Honestly, there is no universal 'right photographer', But there is a photographer right for you. 
There are an abundance of wedding photographers out there, and many are very talented, but on the other hand, there are also a lot of photographers who have conceived their photography dream, have ran out and brought a camera, and now believe they are a professional wedding photographer.
All us wedding photographers had to start somewhere, but you don't want your wedding to be their start. What it comes down to, is that it's your choice, and what you are looking to get out of your wedding photographer is the most important factor. Here's just a few tips that might help you on your journey to finding your perfect wedding photographer.