First off, 23.976 fps and 23.98 fps is the same thing, One is just showed as rounded off to two decimals.
There is some confusion on this 23.98 fps frame rate. Many, if not most prosumer cameras - like the Canon 5D MkII and MkIII, Nikon, Sony, Olympus HDSLRs, GoPro, Sony XDCam and NXCam, Panasonic cameras and such like record 23.98 fps, not 24 fps. What makes it confusing is the the menus in some of these cameras show 24p or 24 fps but actually shoot 23.976 fps.
Further, even some NLEs like FCP or Avid, have 24p settings which are actually 23.98. And, in forums and articles particularly those originating in NTSC countries like the US, people refer to 23.976 fps as 24 fps.
So, why 23.98 fps? What purpose does an odd frame rate like that serve? This is a question many in the PAL world, or those coming from film (24 fps) backgrounds ask.
The short answer is that 24 fps video does not play on 29.97 fps TV sets or TV monitors. But 23.98 fps can be made to play on 29.97 fps monitors. But the whole world does not have 29.97 fps TV monitors, only the US and NTSC countries have 29.97 fps TV monitors. That’s why people from NTSC countries cannot fathom 24 fps video. They only understand 23.98 fps video. And people from PAL 25 fps countries cannot fathom 23.98 fps. They only know 24 and 25.
Where did 23.98 fps come from?
History
Television originated in the US. Initially, there was only live TV (video recording came later). So, there needed to be some way to ensure that TV cameras in studios and TV sets at home remained in perfect sync. The only way for the technology of the day, was to sync to electrical mains. And mains in the US was 60 Hz. So the original fps of TV was set to 30 Hz or 30 fps.
When colour TV came about, a small adjustment had to be made to transmit the colour reference signal. This needed the frame rate for colour TV (in the US) to be set to 29.97 fps. Which is why NTSC is still 29.97 fps. And there’s no such thing as 30 fps any more. Even in HD, 1080i60 is actually 29.97 fps.
In the PAL world, meanwhile, TV began as 25fps since electrical mains in UK and other European countries, was 50 Hz. So, PAL countries adopted 25 fps for TV.
Coincidentally, all cricket playing countries, also have 50 Hz mains - England, India, Pakistan, Bangladesh, Australia, New Zealand, South Africa, Kenya, UAE, Netherlands, even Afghanistan are all PAL and 25 fps. Canada isn’t PAL, and they play cricket, but who really cares about watching Canadian cricket.
Film and TV
What happens to film which is 24 fps? Film has always been 24 fps. Exactly 24 fps.
When film was shown on TV, it was shown using a machine called ‘Telecine’ which converted film to Television. In NTSC countries, this was done by repeating 6 frames every second so 24 fps became 30 fps in the Black & White TV days. For colour TV (NTSC - 29.97 fps), film was run at 23.976 fps and 6 frames repeated every second to get 29.97 fps.
In PAL countries, film was either run at 25 fps (4% faster) to get a 25 fps TV signal, or one frame was repeated every second to get 25 fps from 24 fps. So, in PAL countries film was 24 fps in a cinema and 25 fps on TV. No in-betweens like 23.98 fps.
Digital
When video became digital, it still had to follow existing frame rates. And when SD got upgraded to HD, we still followed old frame rates so that old SD material could be used for HD TV. Today, we have TV sets which can play any frame rate, so there’s no need to have a distinction between video and film rates. But its too late to change now.
So now, we have
1080i50, 1080p25, and 720p25 all at 25 fps
1080p50 at 50 fps
1080i60, 1080p30, and 720p30 all at 29.97 fps
1080p24 at 23.98 fps
1080p50 at 59.94 fps
and there’s also 1080p24 in the PAL world at exactly 24 fps.
Movies are watched in cinemas on digital projectors showing DCPs (Digital Cinema master files) playing out of DCP ‘servers’. These servers support all frame rates, but theatrical ‘film’ is generally 24 fps. At least in all Indian cinemas, and in most film festivals worldwide.
Blu-ray disks are either 24 fps or 23.98 fps. Or even 25 fps.
DVDs are NTSC or PAL, so 29.97 fps or 25 fps.
Professional video cameras like the Arri Alexa/Amira, Red Epic/Dragon, Sony F65/F55/F5, Blackmagic Ursa/Production 4k, Aja Cion and others offer 23.98 fps, 24 fps, 25 fps, 29.97 fps, and higher frame rates. So they offer 23.98 and 24 fps as two different menu items.
How about 4k?
4k also preserves this 23.98 and 24 fps distinction and both exist. 4k cinema DCPs are 4k at 24 fps. And 4k TV, also called UHD (the TV form of 4k) will exist as 29.97 and 25 fps. And even as 50 fps and 59.94 fps.
So that’s the story. 23.98 fps, is not the same thing as 24 fps. Both will be around and both will co-exist. And depending on who you ask, or what you read, some will distinguish between the two and some will refer to only one. And those that refer to only one, will most likely mean 23.98 fps. That’s just the way it is, and for the foreseeable future, that’s how it will remain.