There are four letters in Farsi that do not exist in Arabic - (گ ژ چ پ), which make the 'p', 'ch', 'zh' and 'g' sounds, respectively. But the underlying calligraphic system (RTL order, joining forms, harakat diacritics, and so on) is pretty much the same across the Arabic script and its descendants.
The same issue also exists in Latin script, where German has the ß, not to mention various umlauts, strikes, circles and cedilles modifying letters of the otherwise standard Latin script.
If you live in Europe and speak a language using a Latin script, you probably have come across most of the extensions other European languages add to the shared base in loanwords or foreign media. But then you look at something like Vietnamese and you are no longer sure how letters work.