There are several different wedding photography styles out there but of those styles, there are 5 which are most common. Each wedding photographer has their own style and way of shooting which should be considered when you are shopping for your perfect photographer.
A traditional photographer usually focuses on on poses and even what could be considered candid images. It isn't as though the pictures are forced but that they are posed in a way as to show the beauty and dignity of the image. Traditional photographs are often the ones that you would see in your parents wedding album. Not all photographs taken by a tradition photographer appear posed, there may be a few in the mix that are action shots. Most traditional photographers have an eye for the beauty of the moment and are good at setting up the shot to portray the artistry and excellence of the moment.
A classical or contemporary photographer specializes in well-lit, composed images. They often try to keep out of the way and remain unobtrusive to capture the perfect classical images. These are images like the bride and groom kissing following the ceremony with the sunset in the background or some other "picture perfect" classical portrait. You won't often find a classical photographer asking for everyone to smile, but you will notice them waiting for those perfect images in the magic moments.
A photographer shooting in a photojournalistic style sees the day as a progressive story made up of many special moments. It is their goal to shoot those moments in real time as they happen without interference. They will capture those posed images that you want but their focus will be primarily to photograph the candid and spontaneous events of the day. The photographer will capture close-ups of emotional reactions throughout the day and seeks out the personal moments not orchestrated by them.
Commercial photographers are masters at capturing all the fixed settings such as the cake, flowers, place settings and decor of the event. They are so good at this style of photography that they could be hired just for this purpose. That doesn't mean that they can't take pictures of people, but that they are especially skilled at the fixed components of the wedding day. They may capture the day with more of a formulated approach and don't tend to be as spontaneous as a journalistic photographer. Don't discredit these photographers though because they are still capable of taking high quality brilliant pictures.
The photographer that shoots in an artistic style is similar to a photojournalistic photographer in that they often shoot images that aren't staged or posed. They search for the artistic elements to photograph in people and events. The artistic photographer is often quite skilled in black and white photography and incorporate unique and unusual elements of background and surroundings. Their beautiful photos are likely to be full of drama and artistic quality and less candid.