Is there any difference between a TV and monitor in regard to latency (for high-speed online games such as fightings, sports simulators and FPS) when connected to PS/Xbox via HDMI cable? If there is can it realistically affect gaming performance?
Regardless of your output device or means, TVs were never designed with low input lag in mind.
As you can see from this study TV latency varies from 15ms to 100ms and that is borderline unacceptable for a fast paced game.
In comparison pretty much every gaming monitor's selling point is 1ms, 2ms, 3ms