What is the difference between a partisan election and a non-partisan election?

A partisan election is one in which party labels appear on the ballot.  A non-partisan municipal election does not permit party labels to appear on the ballot.

In a party primary, you must tell your election judge which party's ballot you wish to take into the voting booth.  You will receive a ballot formatted so that you may only select candidates from that party. However, you may still vote on any and all issues, and any non-partisan candidates.