More or less. The original versions of these clauses were usually more explicit, but they were revised around so that the Constitution would not grant explicit recognition of property in people. This distinction was mostly rhetorical at the time, and an issue about which some of the Virginians were squeamish, but it created space for an antislavery theory of the Constitution later on. Of course they didn't know that was coming at the time.

How prevalent was that squeamishness? It's hard to say because it's so trivial that proslavery enthusiasts didn't have a real reason to pitch a fight over it and so force firm lines to be drawn.

In actual practice, the Constitution is extraordinarily vigilant with regard to slave property and that's very much by design. Hence the later antebellum debate between Garrisonian types who took the Constitution (correctly) as a proslavery document and damned it as a covenant with death and people who believed there was more room for constructive engagement within the Constitutional framework. The obvious guy here is Lincoln, but the big innovators on the side where James G. Birney and Salmon Chase back in the Liberty Party days.

Sources

Free Soil, Free Labor, Free Men by Eric Foner

Slavery's Constitution by David Waldstreicher