Why Does the Falchion Look Different?

In the 2000 years since Marth originally wielded the Falchion to end the War of Shadows, the blade was presumably continuously passed down through Marth's lineage, changing in appearance drastically. The discrepancy in its appearance across time is explained by Owain in his supports with Lucina.

Is Chrom's Falchion the same as Martha?

Chrom and Marth have the same Falchion, but Chrom's Falchion got the hilt and pommel replaced, the actual blade is the same (in name if not in design).

How did Falchion get to Valentia?

Mila and Duma's long dispute ended with the formation of the Divine Accord, which split Valentia into Rigel, ruled by Duma, and Zofia, ruled by Mila, with Duma retaining possession of Falchion. ... He obtained Falchion from Duma, and used it to seal Mila away.