I notice you did make the distinction, but I have a few thoughts, anyway.

Whereas in the first case, where "general welfare" isn't modified, it is preceded by the term "promote," whereas in the second case the term "provide" is employed.

Before proceding, I note that the term "general" is used in both cases, and it would seem this is in order to instruct us that it applies to the benefit of all citizens equally, without singling out any individuals or groups - no favorites, everyone is equal.

More specifically,...

....it would seem that the first case is more general than the second, and so since one cannot "provide" for every circumstance that will ever occur, one is merely required to be responsible for "promoting" the general welfare of states and their citizens as befits the times and circumstances, in whatever ways such that each person has an equal potential for benefit, with no prejudice against anyone. Even more specifically, it seems that this refers to ensuring laws that protect members from anything depriving them of their freedom or the fruit of their labors.

...and in the second case, where the govt is to "provide for" the "general welfare" it is here limited to "the United States," a term not used in the first case. what this could mean is suggested by...
(1) - the proximity to "defence" and
(2) - the meaning of "provide" as defined by how it is used in all other occurances of it's use.
{Also, It seems that, since the term "general" is also used here, the Fed govt., may not seek to benefit any individuals or groups more than any other.) Rather, it would seem that the term "provide" means to have in place a well staffed and funded readiness plan so that if any state (not individual or group of same) is in need of assistance in case of invasion or natural disaster, or any other situation beyond it's ability to cope, then that plan could be acted on to assist said state(s) in managing the situation. But, it doesn't at all suggest Federal obligations to "provide" for the needs of individuals or groups. If anything, that could be something a state might decide it needs to do, but not the Fed Govt.

Also, since it is necessary to finance such efforts, we find that requirement in proximity to taxation, which also is modified to make it fair to all the states.

Some people I've seen discussing this in the case of "provide" for the "general welfare" they ignore the fact that in that case the term "the United States" comes to tell us which "general welfare" we are "providing" for, as opposed to "promoting." I notice that you don't make that mistake, though I would argue that we can't invoke, as you seem to be doing, "of the United States" in the first case, because in that first occurance of "gneral welfare" the term "of the United States" is omitted. BUT, in that case the term "promote" is used instead of "provide" in which case it seems to be dealing with the right of equal protection of every individual under law in order not to limit their initiative and productivity, and nothing more.

If you have any additional thoughts and/or good references on this, I would appreciate it.

Regards

P.S., with regard to recent revelations that Obama said that the Constitution is "deeply flawed" because the framers were "blind" and that the "constraints" they placed in it are impeding "spreading the wealth," it seems his goal is to rewright the Constituion or at least to "reinterpret" it out of existence.

Please G-d that doesn't happen.