It sounds like you’re trying to use the same template with two different templating plugins. The Daily Note plugin does not use Templater syntaxes, so Templater doesn’t know what to do with it. At least, that’s my guess.
Why are you trying to open the daily note via templater when the Open Daily Note option works as expected? What are you trying to achieve?
I see - templates and templater is not the same. I was trying to insert teplate by templater icon, which looks 100% the same as Obsidian insert template menu.