Magic Counter is a blue Support materia. You can link it to any Magic or Summon materia and it will cast the highest level spell when damage is incurred. You can indeed win it from chocobo racing at class A and S, and it is here in the Northern Cave.

Counter is a blue Support materia. You can link it with D.Blow, Manip., Master Command, Morph, Mime, Sense, Steal, Throw. The action will then be used when damage is incurred. You'll only find Counter in the Northern Cave on this screen.

Counter Attack is a purple Independent materia. When equipped you will counter with a physical attack when damage is incurred. You'll find one of these after defeating the Materia Keeper in Mt. Nibel and you can win it from the chocobo races at class A and S. Although the prize list shows it as 'Counter', it is the Counter Attack materia.