Semitic languages characteristically pair a plain consonant with an emphatic one, articulated further back in the mouth, and treat the two as separate sounds that distinguish words. The inherited alphabet gives each member of the pair its own letter, and Mandaic keeps them: asz beside as, att beside at, and aq at the nineteenth place.
What exactly emphasis consisted of in the older languages is described differently in different accounts, since the evidence is spellings and later reading traditions rather than recordings, and the modern languages that keep the contrast do not all keep it the same way. In Mandaic the letters are kept apart in writing, and the spoken language has narrowed some of the distinctions, as it has narrowed the gutturals.
The naming scheme makes this harder to see than it should be. Asz and as differ by a letter that stands for nothing; att and at differ by a doubled t that has nothing to do with length. Both spellings exist to keep names apart in a scheme without diacritics, and a reader who takes them as descriptions of the sounds will be misled in both cases.
The pairs also sit far apart in the sequence, at fifteen and eighteen, at nine and twenty-two. The inherited order does not group related consonants, which is one of the things that makes it look arbitrary and makes its survival across four alphabets meaningful.