what is the difference between doppler shift and gravitational red shift?

With Doppler, motion away causes redshift, with gravitational redshift, as photons of energy rise out of a gravitational well, they still move at lightspeed (unlike anything composed of matter), but lose energy in the process (e=hf), so their frequency lowers and wavelength increases, resulting in a shift to the lower energy end of their spectrum, which in terms of visible light is the colour red. There is a lot of conjecture about part 2 of your question. If you knew its mass, and performed a spectral analysis...

Doppler can also apply to sound. (a passing train whistle for example).

Doppler red shift assumes an object is receding from the viewer and its light is shifted. Knowing the shift, one can deduce the speed of movement.

Gravitational red shift? Is red shift caused by light travelling through or from a gravity well (like a black hole). It would modify the doppler shift results by making the source object appear to recede faster than it really is.

We can use other methods of distance calculation to help determine if the red shift has been "tampered with" by gravity. Typically, "nearby" (in space terms) objects have a lesser red shift than "far away" objects. If we can deduce the distance, we can then account for potential unseen gravitational forces.

there is no difference since Doppler effect is measured in terms of red shifts

pricey The Grannyator, The gravitational pink shift of any given star is many times so minor as to be all yet inconsequential. To calculate an merchandise’s gravitational pink shift you opt for to commence through determining it’s mass. LL&P_// ESP