A few days ago as I was getting dressed for work, I heard the rumble of the garbage truck and asked my husband, who was still asleep, "Did you take the trash out last night?" He answered in the affirmative, but it turned out that he hadn't. I figured that his incorrect response was due to sleepiness, but as he later explained, he'd thought that I'd meant, "Did you take the trash [from the kitchen, etc.] out [to the big plastic bin outside the garage]?" I, of course, had intended to ask, "Did you take the trash [from the big plastic bin] out [to the curb for pickup]?"
To me, "take out the trash" describes moving all the trash from inside the house to the big plastic bin. It's such a common phrase in listing chores, along with "feed the cat" or "load the dishwasher", that "take out" has become a phrasal verb of sorts. In "take the trash out", however, "out" is simply a directional specification that could just as easily be replaced with "to the dumpster" or any number of other adverbial phrases.
Obviously, not everyone---my husband being an obvious example---shares these interpretations, and I don't think I have a case for suggesting they should be universal. But it's interesting to analyze what goes on in our heads with little language quirks like this. I wonder if such subtle differences in meaning and intention make up a larger part of communication problems than we think.