Ambiguity of "or"

I have these two sentences:

• We can get ammonia by treating ammonium salts with caustic soda or sodium hydroxide.
• We can get ammonia by treating ammonium salts with lime water or calcium hydroxide.

Caustic soda is the common name of sodium hydroxide, while lime water and calcium hydroxide are two different substances. Both the sentences are grammatically and scientifically correct, but they obviously mean quite different things.

In this particular case, I happen to know how to parse either sentence, but what if I get a situation where I cannot recognise whether the first term is a synonym for the second, or a different term entirely?

I did not come up with this question myself, the first sentence is actually given in the standard NCERT textbook of INDIA. Nearly 1.5 million students are studying using this book. Is there a mistake in our book?

You don't disclose what the book is asking, but there is no mistake in the sentence as such. As you yourself say, both sentences are grammatically and scientifically correct.

That the conjunction is ambiguous, is unfortunate — but that is nothing unusual. Most words in most languages have more than one meaning, and without enough context, it is impossible to tell which one the author meant. When the meaning is impossible to tell, then the meaning is impossible to tell, and further explanation is in order. Not your fault.

In this particular case, the ambiguity in the first sentence can be removed using a simple "also known as", or something to that extent, while the second sentence could be disambiguated using "either... or...":

• We can get ammonia by treating ammonium salts with caustic soda aka sodium hydroxide.
• We can get ammonia by treating ammonium salts with either lime water or calcium hydroxide.

Indeed, a well researched question!

However, there is no way to find out (just by reading the text) whether they are synonyms or hold different meanings. The onus thus completely lies on the writer / speaker, wherein he / she should ensure that the receiver interprets it correctly.

This question's answer is indeed usage learning for writers / communicators themselves, so that they frame statements in a manner which receivers interpret correctly.

For synonyms, the suggestive uses include ''also known as'', ''commonly referred as'', ''aka'' etc. • We can get ammonia by treating ammonium salts with caustic soda, also known as sodium hydroxide. For words with different meanings, even saying ''as well as'', ''in addition to'' may also help depending on the context. • We can get ammonia by treating ammonium salts with lime water, as well as calcium hydroxide.

As the NCERT book is in question, I would recommend offering a suggestion to the book’s editorial team for incorporating similar modifications.