"and don't use in tv the same color map?"
The Wii is spitting out the same color to each device. It is then the device's job to represent color. Neither display is showing it to you wrong, they are just of different color temperatures. In concerns to color, humans are terrible at detecting color resolution, but super-picky about differences in hue when there are two examples sitting in front of them. When only one example is present, we are really good at subjectively shifting color in our brains to the expected values.
In example, a 6500K white-calibrated TV is kind of red. After looking at it for a couple of minutes though we decide that the "pink-white" is baseline white and everything else shifts from that. The purple-blue then internally becomes blue, super-red becomes normal-red, etc. In example #2 a 9300K white-calibrated TV is pretty blue. Again, stare at it for a minute or three and we decide that the "blue-white" is baseline white and our brains shift colors accordingly. Super-blue becomes regular-blue, purple-red becomes normal-red, etc.
Saturation would also be related. Most people have saturation cranked up way too high on their TV. The result is that there is simply too much color layered on the grayscale image. A properly calibrated TV has less saturation than all of our portable devices though. On my Wii U display, saturation is a bit too high and it's color temperature is probably in the 7500K range, or medium-white. My main display is properly cranked down in saturation, and is also set to a medium-white temperature of ~7500K as I play a bunch of games and don't really care about proper 6500K film calibration. The result is that color temperature matches up pretty well between my displays, in that blue looks about the same between them. The over-saturation of the Wii U tablet means that blue is "bluer" though, in that there is just more color present.
So, if you guys want your displays to match, play with your Temperature setting on your TV. The options are usually Warm, Normal, Cool, with Normal as the likely close choice. Then play with Saturation on your TV, probably cranking it up a bit if your display is calibrated, or cranking it down a bit if your settings are on whatever it came out of the box as.
Or you can just say "screw it!" as nothing is wrong and therefore there is nothing to fix.
"but why they are using a lower resolution color map over the greyscale"
Again, humans suck at color resolution. There are just not that many cones in our eyes. As such, a great way to save bandwidth on video compression is to use a quarter-resolution color image layered on top of a full-resolution greyscale image. You've spent the last 20 years staring at quarter-res-color digital compression. The Wii U is doing nothing new in that regard.