When noticing that your mind has wandered how do you make sure that you bring your attention back with with kindness and nonjudgement? Or put another way, what is the difference between this and thought suppression?

It happens a lot specially when we start meditating, but we should just see how the thought came and went automatically instead of being irritated or affected by it, it also contains the answer of your second question as suppression of thought make us put efforts which are totally unnecessary and unproductive, it makes our mind weak and the thought to again disturb us.
so being non judgemental at the time of observing thoughts while meditation is one of the practice which makes meditation peaceful and us happy☺.

My best advice is to not think of your mind wandering as a bad thing, never inherently assume something your body does is bad.