The Shahadah is usually rendered one of two ways:
There is no God but God
That's virtually a tautology. Perhaps the only thing that spares it from pure tautology is the implicit monotheism in the singular formulation. That might be designed to rule out polytheism.
By by itself, it fails to say who God is. It doesn't distinguish the true God from rival claimants. What God does it refer to?
Perhaps, though, that lacuna is supplied by the next phrase: "and Muhammad is his prophet/messenger."
The other rendering is:
There is no God but Allah
That has greater specification. It pinpoints the God in question as Allah–to the exclusion of other named Gods.
That might be what the sentence intends to convey, where the first occurrence of the divine name is generic while the second occurrence is specific. The first occurrence is denotative while the second occurrence is connotative.
But it's striking that we have this semantic ambiguity in the fundamental creed of Islam. What does the Shahadah even mean?