All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
The correct meaning of "There is no god but Allaah" is "There is no deity worthy of being worshipped except Allaah". The correct meaning of "Muhammad is the Messenger of Allaah" is "There is no true Messenger to be followed except Muhammad the Messenger of Allaah, sallallaahu ‘alayhi wa sallam".
Any other meaning is incorrect. For example, some people say that "there is no god but Allaah" means "there is no deity in the universe to be worshipped except Allaah". This is incorrect because it contradicts reality. In fact, there are a large number of gods in the universe that are worshipped other than Allaah The Almighty. Allaah The Almighty Says (what means): {Has he made the gods [only] one God? Indeed, this is a curious thing."} [Quran 38:5]
Moreover, some people say that, "Muhammad is the Messenger of Allaah" means "there is no one in the universe who is followed except the Messenger of Allaah, sallallaahu ‘alayhi wa sallam". This is incorrect because there are some people who follow and sanctify persons other than the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, and they give precedence to these persons over the Messenger of Allaah, sallallaahu ‘alayhi wa sallam.
Allaah Know best.