# Doppler effect - Apparent change in frequency or wavelength?

Hello,
I've been thinking about what exactly is the doppler effect and I'm not sure I understand it because I thought it meant a change in frequency due to relative motion while at the same time its defined in terms of changing wavelength such as in red shift or blue shift.

Case 1
The ubiquitous example is that of a wave source moving toward or away from the an observer emitting waves in the process. If the observer is stationary and the source is moving toward him with speed v_s, since the speed of the wave, v, is determined by the medium, a reduction in the wavelength measured means an increment in frequency.
So in this case, the wave speed doesn't change while the frequency and wavelength of the wave received changes.

Case 2
Let the wave source be stationary and the observer move toward it. With respect to the observer, the wave fronts will appear to be hitting him with speed v+v_s. The wavelength measured is the same and so the frequency has to increase.
So in this case, the wave speed appears to change causing the apparent frequency to change while the wavelength is the same.

Case 3
Let a wave traveling in a vacuum enter another medium such glass. The frequency does not change but since the wave slows down, the wavelength measured in the glass medium is smaller.
So in this case, the wave speed decreases causing the wavelength to reduce while the frequency remaining constant.

I know that case 1 is an example of the doppler effect. Is case 2 an example of the doppler effect ? If it is so, why case 3 is not because I've never heard or read that its an example of doppler effect, but if we say that a star is undergoing a red shift is an example of the doppler effect, then obviously a change in wavelength inside the glass should be considered too. If not, why ? Is it because, doppler effect is defined only as the apparent change in frequency ? If that is the case then, red shift or blue shift are improper terms ?

Thanks