In fact, there is a difference, but it is not big. "(a) Dog" and "(a) Dog" are both quantitative phrases, which consist of numerals and quantifiers.
Grammatically speaking, they have the same structure and function, and they all modify "dog" as an attribute. However, "only" can also be used as an adverbial, only, only dare, only hit you, only kill the devil.
Phonetically speaking, the second syllable of the two is different. Personally, I think the word "only" in A Dog is hesitant, because the tone change is just a quantifier, so the sound of continuous reading is lighter and shorter than that of single reading.
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