What is the difference between a monoatomic and a polyatomic ion?

It's the ions which are monoatomic, not the compound.  

Zn2+   1 atom/ion    
(Cl-)2  1 type of atom/ion

SO4 (2-)  polyatomic
NO3(-)  polyatomic

HTH

Your teacher should have said that each of its (three) ions (one Zn++ and two Cl-) are monoatomic.

An example of a polyatomic ion can be found in NH4Cl (ammonium choloride) or ZNSO4 (zinc sulfate), or of course, (NH4)2SO4 (ammonium sulfate).

The ammonium ion (NH4+) does not break down into separate monoatomic ions of nitrogen and hydrogen; each of the four hydrogen atoms is symmetrically arranged (in a tetrahedral fashion) around the central N and the charged is evenly distributed over the entire surface of the ion.

Likewise, SO4-- (sulfate ion) does not break down into separate monoatomic ions of sulfur or oxygen. It is likwise tetrahedral, but there is a double charge distributed over the surface (note: this is a correction; I previously described sulfate ion as if it were SO2--).

Hope this helps.

Rex, a physician, in the midwest