Nowadays, the term oxymoron is used less often in its literal sense and more often as the punchline to a joke. It is used to draw the humorous (and often not actually legitimate) distinction between two things.
is one well-worn example people use to make fun of the military. Is it a legitimate oxymoron? Of course not. The military makes stupid decisions, to be sure, but they often make very smart ones.
Even legitimate oxymorons rely on different senses of a word to achieve oxymoronic status:
That statement was truly false.
Here truly really means really or absolutely; it is not used in its Boolean sense.
Wikipedia notes this usage:
Although a true oxymoron is "something that is surprisingly true, a paradox", modern usage has brought a common misunderstanding that oxymoron is nearly synonymous with contradiction. The introduction of this usage, the opposite of its true meaning, has been credited to William F. Buckley.
Other oxymorons cannot be dismissed so lightly, however. For example, the fictional creatures known as zombies are referred to as the "living dead." In that case, both meanings apply equally, and a true paradox is presented. How can something be alive and dead at the same time? We have to think of a different kind of meaning for "living", to be sure, but it's still pretty close to the kind of life we mean when we say something is alive (except in most cases normal, non-zombie humans have better hygiene and presumably don't want to eat your brain).