How does that happen? - In accounting for meaning, we try to isolate the phenomenon of meaning. For that end we distinguish between what a sentence means and what it does. But when we make this distinction, we almost always (possibly always) have a clearer idea what we intend by “does” than by “means.”
The unclarity runs deep: We somehow forget that ‘to mean something’ is to do something. Meaning is a subcategory of doing, and Logic treats of action, not of meaning. Our distinction was therefore not completely successful. We did not really isolate the phenomenon of meaning properly.
As a result of this forgetfulness, “meaning” becomes a general name for all the other things that a sentence does - all the things beside what it “does,” the things about which we don’t have any clear idea. Namely, it becomes a waste basket.
We hide that unclarity by assuming that there is such a thing as “the normal use of language,” or “the normal way to mean.” This is supposed to give us a (feeling that we have a) distinct notion of meaning. (Actually, there are supposed to be two such “normal” uses of language: one to state factual truths, and another to express values.)
The only thing that we know about this “normal” way of using language is that it is normal. That is, we think we latched on to some idea, but we haven't made sure it has any content. The truth is that we have an idea without content; that is, we have no idea.
And so, this “idea” doesn’t really give us any distinct notion regarding what we intend by “meaning something.” In particular it doesn’t give us any clear idea what we do with the true-false distinction.