I've heard of trill, but this is the first time I heard mordent. So I went to google it, only to become more confused🤦♂️. The only consensus seems to be that they are indeed to be played differently. But on how to identify which is which by the ornament sign, and which sign means inverted (mordent), I am seeing contradictory answers. I do find this one appears to be more convincing to me.
Faber does not teach ornaments in their book 1. When I first encounter a trill in their companion book piece, I had to figure out on my own. My take away is ornaments are much difficult than they appears, and they need specific teaching and lots of tailored practices to be performed right. I may add and practices them only after mastering everything else of the piece.
A couple of things I learned that apply to beginners. There is natural yet wrong tendency to play trill (or mordent, I suppose) as even divides in time, either because a beginner do not know, or because their fingers aren't that quick. And, there is a natural tendency to tense up before playing the ornaments, but that's exactly the opposite to what's needed which to relax just before the ornament to play it light, fast and fluent. Zhadnov mentioned this in his video on Petzold's Minuet, too.