Re[x] vs. x ∈ Reals in the context of Assuming

Let's say that $x$ is some real valued number $>0$.
Are the following commands interchangeable in the context of using Assuming?

1. Assuming[{Re[x] > 0}, Integrate[...,x]]
2. Assuming[{x ∈ Reals && x > 0}, Integrate[...,x]]

Or, as I suspect, is this not true for the reason that Re[x] > 0 should just mean that the Real component of $x$ is $>0$? Also, is there a way to more compactly specify {x ∈ Reals && x > 0}?

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