A messer is a single-edged sword of the 15th and 16th century, characterised by knife-like hilt construction methods.
A Kriegsmesser in the Kunsthistorisches Museum, Vienna.
Fighting with a Messer and a "Hungarian shield" (Gladiatoria Fechtbuch fol. 55r, mid 15th century)
A falchion is a one-handed, single-edged sword of European origin. Falchions are found in different forms from around the 13th century up to and including the 16th century. In some versions, the falchion looks rather like the seax and later the sabre, and in other versions more like a machete with a crossguard.
Falchion – Italy, 15th century