【Repeat】 , 【iterate】 , 【reiterate】 , 【ingeminate】 can all mean to say again.
【Repeat】 , the word in ordinary use, may apply to what is said or uttered or done again, whether once or many or an indefinite number of times.
【Repeat】 sometimes implies a change in the speaker or doer.
【Iterate】 usually implies one repetition after another, especially of something that is said. There is very little difference between 【iterate】 and 【reiterate】 , except that 【iterate】 occasionally refers to a second saying or uttering or sometimes doing and 【reiterate】 carries an even more emphatic implication of manifold repetitions; consequently the two words are often used together when insistency is implied.
When only one term is desired to make this point, 【reiterate】 is especially appropriate.
【Ingeminate】 , a somewhat uncommon term, implies reiteration for special emphasis or impressiveness. It therefore seldom implies indefinite repetition but rather duplication or triplication for the sake of the effect produced.