They are similar, but slightly different. To repay is often used when talking about money. "I borrowed money from my friend last week. Now I must repay him." But you can also use this verb when talking about favors. "My neighbor gave me some milk, so now I will give him some eggs to repay the favor." "To reciprocate" has a similar meaning, but we use it in specific situations. "My cousin invited me to his house for dinner last month. Now I must reciprocate. I will invite him to dinner at my house this week." or "The businessman helped out your company because he knew you would reciprocate later." Other people here may add some additional explanations. Good luck.

The word "repay' is much more common. The two words have similar meaning. I think of repay as meaning to give back money. I will repay my friend for buying my lunch. I think "reciprocate" is giving something of similar value. A person remembers the gift they were given and wants to reciprocate by giving a gift of similar value on their friend's birthday.