A very important thing to understand about writing is that a script does not equate to a language or vice-versa. To use a modern example: Classical Latin, English, and Hungarian all use the same Latin script.

However, an ancient Roman and a modern Brit would both find each other's written documents basically unintelligible. Even though they use the same letters, everything about the language represented by those letters is different. The Roman and the Brit could probably read it aloud and approximate the pronunciation of the words since the letters are largely used to represent the same sounds in Latin and English, but they would not know what those words meant. Meanwhile, neither would even be able to get that far in Hungarian, where some Latin letters have been assigned entirely different sounds to better suit the Hungarian language.

That hypothetical sticks to just one script with minimal variation. Aramaic, Musnad South Arabian, and Pahlavi are all different scripts. They are related, which explains the similarities, but they are ultimately quite different. Then within the Pahlavi script you have two entirely separate languages, Middle Persian and Parthian, which would face the same problems outline in the hypothetical. The comparison of these three scripts is probably closer to a comparison of the Latin alphabet, the Greek alphabet, and the Cyrillic alphabet. They share some symbols, and a few more symbols are clearly similar to symbols in the other scripts, but to anyone who can read even one of the three, they are obviously different.

In both my examples and yours, the visual similarities are the result of a common source between the different script. In the case of mine, both the Latin and Cyrillic scripts were ultimately derived from Greek. In Cyrillic's case the development of a new script based on the original Greek symbols was an intentional project to better record Slavic languages and spread Christian scripture in Slavic cultures. Latin emerged from adoption of Greek letters by ancient Italians and the natural progression of changing how those letters were written and used over time.

Aramaic and Pahlavi are similar for a similar reason. Pahlavi was the direct product of western Iranians adopting the Aramaic script and altering it to record their own languages (ie Parthian and Persian). Some symbols had to be innovated to represent vowels and other sounds that differed between the different languages. Then, over time, how people wrote Pahlavi symbols gradually changed. This development was entirely unrelated to Achaemenid Old Persian, which was written using an alphabet composed of cuneiform characters inspired by the Akkadian and Elamite scripts. Old Persian cuneiform was abandoned following the fall of the Achaemenid dynasty.

Musnad fits in further up the family tree, so to speak. This is also why I wanted to use the example of the European scripts derrived from Greek. The Greek alphabet and the Aramaic abjad actually share a common root: the Phoenician script. Phoenician and Musnad likewise shared their own common root in the so-called Proto-Sinaitic script, an alphabetic writing system that emerged in Egypt around 1800 BCE as a kind of shorthand for the more complex hieroglyphic system that was in use at the time. This system spread into the Levant quickly and began developing into several new scripts, including early forms of Musnad.

According to some academic arguments, this Proto-Sinaitic script, and by extension Egyptian hieroglyphs, is the ultimate ancestor of all alphabetic scripts in use today.