No, it’s not the same thing. “Druids wear armor made of plant and animal products” would still leave room for a player to decide to wear armor made of metal, perhaps in addition to those other armors. “Druids won’t wear armor made of metal” does not.
Like I initially answered, I rule that the player has full authority over what their own character will and won’t do. Druids in general have a taboo against wearing metal armor, and breaking that taboo may have social consequences - for example, other members of your Circle won’t approve, and may even excommunicate you if they find out. But you won’t suffer any mechanical penalties for wearing metal armor.