So, P mode, ISO 200, 1/60 F4, switch to tv ISO 200, 1/60 and F1.8 ....
OK, now that
sounds weird. Because the ISO is under your control in both modes, the exposure narrows down to aperture and shutter speed, at which point the two exposures above will
In P mode, the camera meters the scene and decides on the exposure all by itself, so unless you applied exposure compensation, 1/60 at f/1.8 is the 'almost' correct exposure. In Tv mode, shutter speed is under your control, but the aperture compensates for that. Therefore, the camera should have selected f/1.8 or a nearby value, not stop down to f/4, that's more than two stops slower.
So, check the exposure compensation value in both settings, also check metering (i.e. if you are using spot metering milimeter changes to the composition can cause this much difference). Under the same ISO, metering, exposure compensation settings, the same composition should yield the same exposure no matter what mode you use.