To be technical about it; an arena is an enclosed area, often circular or oval-shaped, designed to showcase theater, musical performances, or sporting events. It is composed of a large open space surrounded on most or all sides by tiered seating for spectators. The key feature of an arena is that the event space is the lowest point, allowing for maximum visibility. Usually, an arena is designed to accommodate a fairly large number of spectators.
The term arena is sometimes used as a synonym for a very large venue such as Pasadena's Rose Bowl, but such a facility is typically called a stadium, especially if it does not have a roof. The use of one term over the other has mostly to do with the type of event. Football (be it association, rugby, or gridiron) is typically played in a stadium while basketball and ice hockey are typically played in an arena.
(Thanks Wikipedia!)
Essentially, it doesn't matter if the stands are the same size or even if there are just three. However, due to the fact that St James Park hosts football matches and doesn't have a roof, technically it should be called a stadium as oppose to an arena.
However, contray to this, there are many football stadiums in Germany which are labelled as arenas such as; The Allianz Arena, The Veltins Arena and The Imtech Arena. Also, England's Coventry City play at The Ricoh Arena. Funny enough, these four grounds all have sponsored stadium names aswell.