I agree with you in that Aristotle is discerning between two different accounts of substance.
Aristotle does this throughout the entire text which is really confusing, which may tie into what Arjen thinks about Aristotle, in that he is always contradicting himself. As soon as you read into chapter 2, Aristotle posits even more accounts of substance (i.e. that it seems to belong to bodies, geometric shapes, etc.), and really doesn't arrive at any really solid conclusions until zeta 10!!! This is basically a transcript of Aristotle troubleshooting the issue and writing down his misconceptions as he goes along.
But anyway, your impression is right, and I agree with you. But I think the issue is in your conception of the thing itself and its predicates with the Socrates example.
For substance at this point, Socrates is Socrates is fine. A rock is a rock, a tree is a tree, an apple is an apple.
That Socrates is a man, mortal, lover of wine is problematic. These seem to be incidental properties of a substance (at this point), that is, they are not primary attributes. Aristotle is seeking primary substance in a primary sense, like the physical attributes of Socrates that are immediately apparent.
That attributes depend on substance, but substance not depend on attributes? You are exactly right on in your deduction and I completely agree with you. That ties in with the second paragraph where Aristotle stabs at the heart of the matter, the underling substance.