Actually, the meanings of both patsis are not totally unrelated. If you are in a room, you open a door and you get... out of it. The word was pats i (բաց ի) in Classical Armenian (the two words became one in the modern language), meaning “out of,” with equivalents in Latin ex and Greek ex, from which today we have English ex (only with the meaning “out of,” as in excellent).
As the reader should know, Armenian nouns have kept declension (khonarhoom / խոնարհում), like in the German language. The case of patsi requires that the word be used with the noun in the ablative mode, which is coincidentally called patsarragan (բացառական) and consists in the addition of eh (է) at the end of the noun: for instance, kirkeh (գիրքէ), tooghteh (թուղթէ). We also add a n (ն) when we need to use an article (e.g. kirkehn “of the book”). For example, patsi kirkeh me (բացի գիրքէ մը / “except for a book”) or patsi kirkehn (բացի գիրքէն / “except for the book”).
We use patsi as a preposition, in the same way that we use “except” in English, but the flexibility of Armenian allows bringing the book behind the noun and turning it into a postposition: tooghteh me patsi (թուղթէ մը բացի “except a paper”).
Strangely enough, people tend to make mistakes when using patsi. They do not decline the word, as in the following sentence:
Pan me chem hisher, patsi poghotsin anoone (Բան մը չեմ յիշեր, բացի փողոցին անունը) “I don’t remember anything, except for the name of the street.”
This may be or may be not influenced by English grammar, but in any case the correct use should be:
Pan me chem hisher, patsi poghotsin anoonehn (Բան մը չեմ յիշեր, բացի փողոցին անունէն).
The rule has no exceptions. The meaning in English remains the same, but the accuracy of the Armenian original improves a lot.