This is what my Windows accent color looks like on both monitors, as captured by my phone's camera. The colors don't actually look like this to the naked eye, but it shows how different the tones are.
I've got them set up as dual monitors and it's a bit jarring to go back and forth between the two. Back when my old monitor still worked I think the difference between it and my TV was actually pretty similar, but I've only had the TV for so long I've gotten used to its color palette. I assume TVs and PC monitors might just have different color temperatures in general.
The AMD control panel logo shows up as a deep red on the TV, while on the monitor it has a purpleish, magentaish hint to it.
Tried messing with the AMD control panel settings to get the monitor to match the TV more but I couldn't really do it. I don't really have an eye for this sort of thing so it might very well be that my TV's color settings are a giant mess anyway so I guess I'll live with it 
Research the panels used in them. Most TVs use PVA or IPS panels which usually have better color accuracy than cheap monitors (and some expensive gaming ones too) that use TN panels. TN has historically had better response times than IPS/PVA, but that's not a big of a deal these days outside of gaming uses.
The panel type also effects viewing angle and color shift due to off-angle viewing. I'm assuming they are both LCDs and not OLED or Plasma or some other less common tech. If they have different types of panels, color match is almost impossible across the gamut. It can still be impossible with matching panel types depending on the specific models.