Yes, it's the qualification - or rather, the quantification - that makes the difference; it becomes a bundle of statements, rather than a single one.

I'd forgotten to mention the other use of "if...then...", with the consequent in the imperative - i.e., the procedural use. You can, actually, interpret strict implication that way too: "if you learn that A is true, conclude that B is true". (OK, it's a bit of a stretch....)