Diagnosis
The projector is likely receiving a limited RGB (16-235) color range signal from your PC, while your TV is getting the full (0-255) range.
How to Fix It
On your Windows PC, go to Display Settings -> Advanced Display -> Graphics Settings. For the projector, set the output color format to RGB and the dynamic range to 'Full'.
If That Didn't Work
Check the projector's own picture settings. Ensure 'BrilliantColor' is enabled and that the Color Profile is not set to a muted preset like 'Presentation'.
Heads Up
If you're using an NVIDIA GPU, also check the NVIDIA Control Panel under 'Change Resolution' -> 'Output Color Format' to verify it's set to RGB, Full range.