Campgems is right about the metallurgy being different. There is a simpler way to test though. Just bend it. Piano wire is spring tempered and can be bent a lot and will straighten right back out. You'll feel it give smooth resistance and you start to bend it then stiffen up as it reaches its maximum bend, after which it will take a permanent set if you keep going. Mild steel wire will give very little resistance and take a set with very little bending.

If you need the wire to do anything but be a place to screw on your clevis then you need the springy piano wire. It is much stiffer and nearly impossible to stretch. That's what makes it useful for piano strings; you can put a ton of tension on it and it will just hold it there without stretching, then it is springy enough to vibrate for decades without breaking.