Satan and the anti-Christ are not the same thing although many people come to that conclusion, but I don't think the Bible says that at all.I suppose one would need to do a thurough word study in order to get a better understanding of those verses. Especially on "grave". Satan embodies a man, in the anti-christ, to lead many kingdoms astray, does he not?
Lucifer and Satan are the same. ...
Just my opinion:
Angels walked as men amongst humanity on a common basis and I still believe Lucifer and Satan are one in the same.
The Name Lucifer is literally translated light bearer or brings light. Compare that with the following verse:
2Co 11:14 And no marvel; for Satan himself is transformed into an angel of light.