Even if the color looks different in different screen, they are the same. I mean, for example if you are using a red color RGB 176,19,19, it's going to be always that red, but in your screen, in your laptop, in your phone, or mine, or any of those who are reading this post in their screen, that exactly same 176,19,19 doesnt look exactly the same red. In my case, i'm using right now an imac and a bosto tablet to draw, and a purple color is looking blue in the bosto screen.
You can try to calibrate so they may look as close as possible, but don't get mad. Instead of make all the work over the tv's and then check out in the laptop, what you can do is to duplicate the canvas of your drawing, your laptop`s screen will be your "master/reference" color, and the tv's screen the place to work. And as long as you're working, you are having a look at the laptop to see how's looking.