Contact, touch mean the state or fact of coming into direct connection or close association with someone or something.
Contact implies the mutual relation between two bodies that impinge upon each other.
Touch primarily implies the action involved when a tactile organ, especially of a human being, comes in contact with someone or something or the sensation involved when one feels through a tactile organ the presence of another person or object.
Although these two words are often interchangeable in general use, contact may be preferable when the intent is to stress a connection or association whether between bodies, between persons, or between persons and things and the sensation or emotional response is not emphasized, or when an impersonal or unexplicit word without clearly defined connotations is wanted.
On the other hand touch is usually preferable when the idea of the sensation or of the emotion involved is more important than the abstract or literal idea of coming into contact or when lightness or delicacy is to be implied.