Nowadays, to the average consumer there seems to be little to no difference between a TV and a computer display monitor. They look the same, they use the same technologies, they use the same resolutions and refresh rates, they have HDMI input... The only difference seems to be physical size. When computer display monitors, even 4k ones, have typical diagonal sizes of about 24-32 inches, TVs tend to have diagonal sizes of 40, 50 and even more inches.
If you are purchasing a new display primarily for gaming, even (or especially) if it's console gaming, which kind of display should you purchase? After all, a huge 50-inch 4k TV sounds enormously cooler for gaming, especially for console gaming, than some tiny 27-inch 4k display. And with the prices of both types of display coming down by the month, the TVs aren't necessarily even any more expensive than the computer displays. (Indeed, you can already find both decent 4k TVs and decent 4k monitors in the ballpark of 500€, sometimes even less.)
So what is the difference between these two types of display, besides physical size? Does it make any difference?
There indeed is one relatively crucial difference. And it's something that TVs very rarely advertise in their technical specifications: Response time.
Response time is the average time that it takes for a pixel to change its color.
With computer monitors, modern TN panels have extraordinarily fast response times, down to 1 millisecond, sometimes even less. On the other hand TN panels have horrible viewing angles, especially vertically. IPS and VA/AMVA panels (which are becoming more and more commonplace, also with TVs) have significantly better viewing angles, and their response time is typically 4 milliseconds, sometimes less (and sometimes more, depending on how cheap the display is).
TVs, on the other hand, have typical response times in the 10-12 millisecond range. That's almost four times the response time of a modern IPS computer display.
The side-effect of a slower pixel response time is ghosting. The pixels are simply slow to change colors, and thus moving details leave a faint "trace" behind. With 10ms it's really subtle, and especially with lower framerates (such as 30 fps, which is your typical movie framerate) it's almost unnoticeable. However, with higher framerates, like 60 and above, and very fast-paced movement it can become visible.
With a 4 ms response time ghosting is essentially unnoticeable (unless you go much higher than 60 fps, which most IPS panels do not yet support). With a TN panel with 1 ms response time there's quite literally no ghosting, even if you go to extremely high framerates, such as 144 Hz.
There may be another drawback in using a TV for gaming: Latency.
Most TVs post-process the image they receive in various ways, and this post-processing may introduce a delay in displaying the picture. This delay may range from 1 to half a dozen frames. The longer this delay is, the more laggy and slow to respond the game will feel.
Some/many TVs will offer a so-called "game mode", which will make it eschew using any post-processing and display the image as quickly as possible. This may fix the latency (or reduce it significantly, eg. to just 1 frame) and should always be used when playing a video game.
Needless to say, computer displays do not have this kind of latency (other than the minimum amount introduced by vsync, but this is not the fault of the display per se.)