Sorta, kinda. This actually gets quite complicated.
It's not so much about the video being at the same rate as the display - the display will invariably sync to the signal it's fed by the computer or decoder. It's about the video being at the same rate as the signal.
On a computer, for instance, you pick a display mode when setting the thing up, the computer then works at that frame rate regardless of what you do with it, and all the video you then watch is forced into the resulting frame rate with frame duplication. This is sort of OK when you're showing (say) 25hz material on a 50hz or 100hz display, or 30hz material on a 60hz display, but it gets a bit messy if you have (as is very common) a 60hz display with 25hz content on it. This happens all the time and it isn't usually that objectionable. Mostly. Er. It's not great.
As such, if you're watching netflix on a computer they can do what they like as precision per-frame display isn't really possible. I'm not sure what they actually do, mind you.
TV decoders (whether built in or external) tend to set up their output signal to suit what the currently-viewed signal is doing, meaning that the content, the signal to the display, and the display are all doing the same thing. A TV channel will have picked a frame rate at some point. I assume that, for instance, a channel dedicated to movies would broadcast at 24p (or 48i segmented frame, more likely) and the receiver chain should follow that. There are 720p 60Hz sports channels and 1080p 29.97hz channels in the US.
I'm not sure whether current broadcast standards allow channels to switch frame rates on the fly, or how most consumer gear would react if they did. Certainly the tech to do it exists.
Bear in mind that NTSC-region DVDs of "cinema" content always were encoded at (strictly speaking) 23.976fps, and the DVD players did the 3:2 pulldown, to avoid wasting bandwidth encoding duplicated fields. PAL-region DVDs were always encoded at 25fps and no special treatment was required and there were 29.976 modes for NTSC DVDs of content originated at video frame rates.
Things like YouTube and Vimeo support a huge range of frame rates, depending what you fancy (though last time I checked, which admittedly was a year or so ago, YouTube didn't support much more than 30fps, so you couldn't do HFR on it).
There is a whizzy new technology called G-sync which is intended for video games, where frames may be rendered by the games machine or computer with variable per-frame timing depending on the complexity of the scene. With this technology the monitor will accept updates whenever they're available, often up to a maximum of above 100fps, which pretty much solves all your problems...
This is a bit of a crapshoot right now.