Yes, there is.
"Eu quero outra maçã" means I want another apple. If I hear that I would understand that into two ways: (01) you have an apple with you and you want to change it for another for some reason. Because it is rotten, for instance. Or (02) you have an apple with you and you want one more. So you will have two of them.
"Eu quero mais uma maçã" have one straight meaning: you want one more apple. You ate one of it, it was delicious and now you want one more.