Alright, let me try to explain it more.
In the beginning, there was one Falchion, which was Marth's. However, in the same game, there is a fake Falchion. So far, that's two.
Then in the 13th game, the original Falchion gets old and rusty, and becomes the Sealed Falchion which is much weaker. After a point, you get the Parallel Falchion, which is a direct copy of the original; but not the same.
Finally, the Sealed Falchion regains it's strength and morphs into the Exalted Falchion, which is stronger than the original.
The Falchion is the only one with those properties that you mentioned. Not the Fake/Parallel/Exalted.
(Also, the Falchion is always capitalized in the games)