The iPad uses AirPlay, which is Apple name for 'casting' whatever is shown on the display of a portable device onto another device, like a TV.
Sadly, the iPad doesn't support full Miracast, unlike most smart TVs.
As of this time, the only way to hook up your iPad to your TV wirelessly is by purchasing an Apple TV. You can also get an HDMI adapter if you don't mind the cables.
Some apps like YouTube do allow you to cast what's on the display to a smart TV, but it is very limited and you'll need an Apple TV or the HDMI adapter if you want to cast whatever is displayed on the iPad, from the home screen to every app that is installed.