A list of Mandaic letter names contains both in and ain, and nothing in the names themselves says that one is an inherited letter and the other a late borrowing. The distinction is worth setting out plainly, because a reader meeting the two in a table will reasonably assume they are variants of one another.
In is the sixteenth letter. It stands where Aramaic, Hebrew and Syriac have ayin, it descends from that letter, and it has been in the alphabet for as long as the alphabet has existed. In Mandaic it also carries the vowel e.
Ain is the last sign in the Mandaic range of the modern character standard. It is a borrowing from the Arabic letter of that name, taken in for the sounds of Arabic words, and it is not one of the traditional twenty-four. Its presence records what centuries of contact did to a small liturgical language surrounded by Arabic.
So the two signs share an ancestor at several removes, since Arabic ayn also descends from the Aramaic letter, and they arrived in Mandaic by completely different routes and at completely different times. One was inherited with the alphabet and one was borrowed back from a neighbour many centuries later.
The atlas records the pair with a relation marked as a conflation rather than an equivalence, which is the honest shape of the fact.