The Schlagers (or schlaeger) used in SCA rapier combat are from the German Mensur or "fraternity dueling" developed in the 18th century. Specifically the practice weapons from this form. The schlager blade was originally seized upon as an SCA rapier simulator because it was the only commercially available blade that approached the form and function of a period rapier. Fortunately this is no longer true, but many people still have Schlagers and some people still buy new ones because they are considered to be less expensive than reproduction rapiers (in actuality the less expensive reproduction rapier blades can be purchased for the same price OR LESS).
Mensur is a slashing form. The idea is to slash with the blade or tip to draw blood. The schlager blade was designed with this in mind. A schlager maintains a constant width and thickness of the blade once you pass the ricasso, this makes the blade somewhat tip heavy which lends itself to quick slashing movements.