Why not a 50-135mm zoom lens?

I do beleive you're right. I found these defenitions of varifocal lens:

Varifocal Lens
A projection lens containing movable elements to permit focusing of the image by varying the focal length. (Not a zoom.)

Varifocal lens:
Contains several movable elements to permit manual adjustment of the effective focal length. This type of lens allows you to adjust the size of your field of view.

So a varifocal lens is similar to, but perhaps not exactly the same, as a zoom lens. Note that one of the defenitions concerns projection lenses.

Thanks for the info!