Nur is an adverb which can mean any of the following: only, merely, simply, solely.This can be confusing when an English speaking student is learning German. Also, there are many other examples of words in the German language that can have more than one meaning. How do you 'unpack this problem'?
I am not sure how this is a problem when the examples you have given are synonyms.
Only/merely/simply/solely basically communicate the same concept in English as well. For example, the following sentences would have the same basic understanding too: - It is only a dog - it is merely a dog - it is simply a dog - It is solely a dog
Nuance is provided by context and stress. .