Welcome to Android Central! A "smart TV" isn't necessarily Android-based -- it's just a TV that has apps you can use. Android TV is an actual Android device that hooks up to your TV (or is integrated into the TV) with an interface that is optimized for media consumption.
I'd be very cautious about buying an Android TV box, though. The vast majority of them are no-name or off-brand devices direct from China, with minimal to no support and a high risk of glitchy firmware and hardware. One of the more common questions on this forum is about frozen Android TV boxes. I'd say the only really reliable Android TV box to consider would be the Nvidia Shield TV.
My suggestion would be to get a Chromecast (which is really cheap) and cast media from your phone, tablet, or laptop to your TV.