Both words refer to dishonest acts, perhaps even the same act, but portray the act in different light. To betray means to violate loyalty. To cheat means to gain an advantage by dishonesty and guile.
If a king tells his minister "You have betrayed me." he means that the minister has committed a gross violation of his duty to his king. If however he says "You have cheated me." he means that the minister has tricked him to gain some advantage, perhaps in a personal matter such as the sale of a horse.
Adultery is both. It is a betrayal because it is a violation of the principle of loyalty to one mate. It is cheating because of the stealth and deception with which it is usually accomplished. Both expressions can be and are used, though the second may be more idiomatic at the moment.