When searching on Google use: "Hide personal results" so that you properly mimic what moz picks up.
In moz look to see if your ranking are for an image, local or general serp. There should be an associated icon with your rank position.
Lastly, we have found that Moz rank positions are rarely spot on with Google. They can show general trends - you are on or around this rank, but rankings change frequently and Moz updates weekly. There is bound to be a discrepancy.
Yahoo and Bing positions for us are not even close. These sites are less of a concern, but we consistently find huge variations between MOZ reports and the engines results on the day of the MOZ report run. It is not uncommon to find that the MOZ report simply fails to report anything.