These are referring to the same thing. The induced velocity is the change in air velocity due to aerodynamic interaction with an object. The downwash from a helicopter is the vertical component of the main rotor's induced velocity. This is the induced velocity of a bunch of rotating wings.
A wing on a fixed wing aircraft produces induced velocity too, but it's located in a region of lower induced velocity during flight. The induced velocity varies in space and time. As a fixed wing induces velocity in the flow field, it "flies away" from that region. So it's flying in "cleaner" air. An exception would be if a fixed wing could fly in a tight circle. In this case it would fly through more of its induced velocity, experience more induced drag like a helicopter, and have a large downwash below the circle.
Another way to say this is that the fixed wing's induced velocity is more spread out in space, and hence not as concentrated at any one point. The hovering helicopter's induced velocity is highly concentrated in the region around the helicopter.
You can probably find visualizations or animations of vortex lines on the web. In those, you will see that a fixed wing primarily trails vortex lines behind it, while a hovering helicopter produces a helix of vortex lines below it, but close by, which keep the induced velocity at the rotor disk high.