There are two selections for movespeed on the trade search, one is for Explicit movespeed, and the other is for Crafted movespeed.
I was curious why my boots with 80 life, 40 ES and 60% resists werent selling, so i went and searched the stats with no results.
Remove the movespeed and there they were. Discovered the Explicit vs Crafted distinction after that.
There is currently no pseudo stat for movespeed in the search function that would cover both like it does for resists/life/etc.
Noted, will get a pseudo mod added for this.
EDIT: This has been added now, you may need to clear your cache first for it to show up.