Do smart tv's or Roku sticks still use internet when the tv is shut off?

I am wondering in the smart tv's or Roku sticks/Amazon Fire sticks are still able to use the internet while the TV's are turned off?? 🤔  I Started with the 100gb plan and it was just fine and now we had to upgrade and the 200gb is used up somehow before our last few days we have before it Renews.. it just makes no sense to me how I can use that much when we are away from home all day and everything is off? I need suggestions..