This statement in the preamble was originally We the people of the States of.... and was changed by the committee on style to make it shorter. This one change made all the difference between the belief of the States versus the people/Federal government.
No matter the style of the wording, they had just created a constitutional system in which citizens are both. They are part of We the People of the United States, the sovereign body of the whole people, under God, and they are also citizens of their respective state. E pluribus unum, and all that.