The label “centrist” seems to be a relatively recent label in the American political landscape. You still don’t see it used much. When you do, probably the most common mistake people make is to believe that “centrist” is just another way to say “moderate”. Nothing could be further from the truth.
A moderate is not an extremist by any sense of the measure, and tends toward more “middle-of-the-road” in their views, but is still aligned with their particular party and still generally holds to the party line. There may be some deviation, but in general. In other words, a moderate is still a conservative, or a liberal, or whatever.
A centrist, on the other hand, makes great strides to not be affiliated with any party, and strives to look at each topic as an individual topic, free from any party line or influence. A centrist will consider arguments from the right and the left. A centrist wants solutions, and doesn’t give one whit from which party the idea originated. This does not mean that a centrist cannot hold strong and/or extreme views. Not at all. They can, especially on individual topics they happen to be very passionate about. A centrist, in fact and in contrast to a moderate, is more likely to hold strong views. They are just not likely to hold an extremist party line all on one side. An overall balance of conclusions is usually the end result. Centrism doesn’t describe an established ideology, centrism describes an independent thought process.