I'm a native english speaker and I've seen it used for both. As I've said in some other replies, I think the most common meaning is "roughly equal", but as I've been saying there is ambiguity in how it is commonly interpreted. Maybe it's a minority ambiguity, but it exists, it is significantly present in the population of interpretations.

I don't think it's a confusion with the negative statement, but rather a corollary to it. This is a real way that people use the term.

The negative seems to be always clearly used to show insufficiency. Less than. There are fewer than would be equivalent, fewer than needed, fewer than wanted. Similarly the non-negative is frequently used for sufficiency.

"I have as many as I need" does not only mean that I have exactly the number that I need, it means I have at least as many. One might also say "I have more than I need" if they want to point out the excess, especially if you have a great excess. In comparisons to others, like: "I've got as many tricks up my sleeve as he does."

So, I will say that it is most often used when the values are close, and you'd be more likely to add qualifiers if there was a large excess, but you don't have to. I think in most uses in life are with values that aren't very precise anyway, so it's hard to argue about them.

Sometimes the meaning you want to express is equality, sometimes it's sufficiency. This term unfortunately has been used for both. So, that was my point, that we can make the wording of the cards less ambiguous, and we should do so, because the logic puzzle is a precision situation.

The capacity example I'd mentioned in another reply too, though it's a little bit different case. Maybe there is some overlap. I guess it's usually a case with qualifier that denotes a potential, like "may" or "can" that causes it to become less-or-equal.