If you have colour management turned on, and after rendering apply an sRGB profile, the hardware should then be able to correctly display the image. From there, the issue is more about correctly setting up the hardware.
Even on the manufacturer’s default settings, there is no guarantee the image will display the same on the TV and monitor, due to differences in white point, black point, brightness, contrast etc. The image could also appear differently depending on the ambient lighting.
In short, the difference is more likely because of the way the display devices are set up. You could look into using a hardware calibration device to set up your monitor, and if you use the TV as a monitor, you should be able to create a profile for that too, as it is effectively a display device, like your monitor.
There is more information on Blender’s colour management and monitor profiling and calibration in the wiki:-