Specialization is separate from learning the style.
The specialization gives you +2 dice to your pool when using that style of martial arts, usually this means using the maneuvers that you have learned for that art (This costs 1 skill point at character creation or 7 karma after) And to clarify, your GM decides if you can use this bonus for anything that is not a maneuver associated with the art (Unless future errata changes this), and may rule that just because you specialized in boxing, you don't get an extra 2 dice when punching someone but you would get it with the Haymaker maneuver you learned with Boxing. Again, GM call on how far it goes, but at least applies to the maneuvers you have learned.
Learning the style (Which has a separate cost of 7 karma, during or after character creation) grants you access to additional maneuvers that are associated with the style, here is where you get one maneuver for free and learn future maneuvers at a cost of 5 karma apiece. Note, some maneuvers can not be used until they have been learned.
Yes, I know it is a bit confusing.