On paper they might have similar meaning but nowadays there is a clear difference in usage between the two. You would use them in different contexts.
To iterate means to do or say something for the second or more times ( repeat). It is an obsolete word now but when used it is mostly for actions, procedures .
They will iterate the steps until they find the solution
I asked him to iterate ( say again) his advice.
We will iterate this procedure until we see the flashing light.
Reiterate as a word has gained a momentum recently. It’s a broadly used synonym but you wouldn’t use it in the examples above. To reiterate means ( mostly) to say something again ( iterate) for emphasis. You stressfully iterate. Other synonyms: emphasise, reemphasise, stress, restate, repeat)
Ok, it’s like talking to the wall. Let me reiterate. I don’t want to attend his wedding.
I really felt I had to reiterate my point that if they don’t practice, they will fail the exam.
The politician wanted to reiterate the key point of protecting the environment.
I reiterate ( repeat) , don’t come here in shoes!
In academic essays reiterate is used frequently as it sounds ‘ smarter’ . ‘I would like to reiterate
the importance of protecting the environment’
*Iteration has an additional popular meaning in computer science ( repeating steps/ instructions) and mathematic ( repeating functions by using the output of one step as the input of the internation)