This term fell out of favor as too vague, until we understood that there's really no better word for it.
These are not extraterrestrials - they're more like gods descending from Olympus, except the gods don't necessarily recognize us as sentient beings. An Alien is any Samsaric Manifestation of a Moksha. They take many forms: Small Greys, Tall Greys, Nordics, whatever. They vary so much because they are going off of logical descriptions of our appearance and don't really care about blending in much. If they could conduct their Psychochirurgical Campaign without legs and fingers, they'd show up without them. But as it stands, an Alien is simply a crude good-enough shell for a non-spatial non-chronological entity to occupy temporarily while it amends a mind in order to perfect the Timeline.
Why are they so hard to document? Because they only need to enter the target's reality.
The conventional ideas about what an alien and an abduction are are Paramemes that leave our conception of reality just a little more intact than if we knew we had been touched by gods.