how do I know if I have a third generation or higher apple tv

… but with a white circle around the menu button.

Since the introduction of the revised model Siri Remote, that model remote has also been shipped with the Apple TV HD (4th generation). It can therefore not be used as an identifier for the Apple TV model.

Identify your Apple TV model - Apple Support

Welcome to the Apple Community.

A third generation model has the older remote (buttons only)

A fourth generation model has the newer remote (buttons and touch screen)

A fifth generation model has the newer remote (buttons and touch screen) but with a white circle around the menu button.

There are other ways to tell too.

Well that's strange, I bought a 4th generation model for my son a few weeks back and it came without the circle. I know this because he text me to complain about it.

FWIW, my Apple TV 4 (HD) has the white circle around the menu button. I checked because that is the fist I have heard about the white circle.

So maybe something changed?

Have a nice day.

Perhaps I got some older stock, but one wouldn't have thought so, I always buy from the Apple store (online mostly - but definitely this time)