Asymetrical and Directional are 2 different and independent things.
Asymetrical means non- symetrical - the 2 halves of the tread are different. These will always be marked with "This side out" or words to this effect.
Directional means the tread pattern is significantly different relative to the way the tire rotates. These will always have an arrow indicating the direction of rotation.
PLEASE NOTE:
It is possible to have tires that look asymetrical - or directional - and not be so indicated. This means that the tread pattern, while have the appearance of asymetry - or directionality - doesn't actually have the performance difference that a true asymetrical - or directional - tire has.
AND!!!!
It is fairly rare for a tire to have both asymetry and directionality.