Open the TV's Settings, go to System (or Device Preferences), then About. If you see an "Android TV OS" version, your TV runs Android TV or Google TV. To tell them apart, look at the home screen: Google TV shows Google TV branding and your Google account icon, and Android TV shows a simpler layout.
Look for "Android TV OS" in Settings
Sony documents the check for its TVs: Settings → System → About → Android TV OS version. Older models list it under About → Version. Sony: which Android version is on my TV? Other brands use similar menus, so the exact names may differ.
If you can't find any Android TV OS version, your TV probably runs a different system, like Samsung's Tizen, LG's webOS, Roku or Fire TV.
The home screen tells Google TV from Android TV
Google TV is the newer interface, and it runs on Android TV OS. On Google TV, the home screen shows Google TV branding and a profile icon for your Google account. Android TV typically shows a clock or settings icon in that spot instead. Sony: Google TV, Android TV or other?
For a phone remote, both count. Apps made for Android TV work on Google TV too.
The brand on the TV doesn't tell you
Many brands sell Google TV models next to models with other systems. Two TVs from the same brand can run different software. Check the settings, not the logo.
If a streaming box gives you the home screen, check the box
If your home screen comes from a box or stick plugged into the TV, the box is what your phone remote talks to. The Remote works with Google TV devices that support the Android TV Remote Service, including Chromecast with Google TV and Google TV Streamer. Google's streaming-device remote guide A Fire TV Stick runs Fire OS, not Google TV: see the Fire TV answer.
One more check for The Remote
The Remote works with Android TV and Google TV devices that support Android TV Remote Service v2. Here's what Android TV Remote Service is. Available controls vary by model and firmware.
It's free for Android phones (Android 8.0 or later), with no ads and no account. Download the app