The bible dictionary defines Antichrist as:
"A word used by John to describe one who would assume the guise of Christ but in reality would be opposed to Christ. In a broader sense it is anyone or anything that counterfeits the true gospel or plan of salvation and that openly or secretly is set up in opposition to Christ. The great antichrist is Lucifer, but he has many assistants both as spirit beings and as mortals."
There isn't a definition given in the bible dictionary for what an Apostate is. but the guide to the scriptures describes Apostasy as:
"A turning away from the truth by individuals, the Church, or entire nations."
So it would appear that we have two different definitions, one pretends to be, but secretly isn't, the other simply turns away. But then there'e this scripture in the Doctrine and Covenants:
"And after they have fallen asleep the great persecutor of the church, the apostate, the whore, even Babylon, that maketh all nations to drink of her cup, in whose hearts the enemy, even Satan, sitteth to reign—behold he soweth the tares; wherefore, the tares choke the wheat and drive the church into the wilderness." (D&C 86:3)
So now we've got two words describing one person. Lucifer is apparently both and apostate and and antichrist.
My question is, what is the significant difference? Can you be one without being the other?