Hi Chong , Plantsman/Plantswoman in English English would denote an expert in Plants with a passion for the subject. To be correct I could use Plantsman/Plantswoman or Plantsperson. Planter would be in US terms a container to put plants in , in English terms it would be a person who plants.
I think that's all correct, I speak UK English and Canadian English and I'm working on US English
Best Wishes
Steve