Am having the same issue. Tried everything. I want only my incoming calls to ring and vibrate, but all others to remain silent without a single vibration (but only visible on screen). It seems that impossible with Samsung.
Besides all of that, I am unable to disable the vibrate with an extra tap on the down rocker. Thought maybe a setting got changed, but can't even find a setting. Note 9
Goto settings, select notifications, scroll down to messages, and select it, next select new messages. Under the new messages tap on it, this will take you to a sub menu, you will notice vibrate is turned on. Click it and you will no longer get vibrations when you receive a new text.