There can be multiple reasons why a plant can be unique to its specific tank, such as due to size, color, or even due to how you were able to get it in the first place. Since everyone's planted tank story is completely different and unique, I'm very curious on yours.
For me, it would have to be my corkscrew vals. They are a basic plant, but I've had these for years and it took me a long time to hunt them down in my own state. I remember just trying to grow them and the would always shoot off multiple runners, where the runners would grow extremely fast but then the parent plant would die off. It seemed like every few months my vals were moving all around my tank as they kept doing this. People who would visit would always ask why do I only move them, but my answer would be "I really don't, they have a mind of their own". To this day some of the runners and parents still do this (which I can't seem to figure out why), but it would be my most unique plant in my tank for sure.