It seems there is some misunderstanding. We do not say "..을/를 무슨 뜻이라고 해?".
What you mean is probably "..을/를 뭐라고 해?", which is commonly said.
"..이/가 무슨 뜻이에요?" means "What is the meaning of .." or "What does .. mean?" (literally "What meaning is ..?"). In all cases "what" is the subject.
In "..을/를 뭐라고 해?", 해 (하다) means 부르다(call), 말하다(say), or 간주하다(consider). So the sentence translates to "What do you call ..?". You can see that the ".." part comes in the position of an object.
So it is the difference of "What is..." and "What do you call...". The meaning is not the same as you can see. You can call an object or a concept something (some word, label) but that "something" cannot be the word's meaning itself.