The Expanding universe is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. Technically, neither space nor objects in space move. Instead it is the metric governing the size and geometry of spacetime itself that changes in scale. Although light and objects within spacetime cannot travel faster than the speed of light, this limitation does not restrict the metric itself. To an observer it appears that space is expanding and all but the nearest galaxies are receding into the distance.
Redshift
In physics, Redshift is a phenomenon where electromagnetic radiation (such as light) from an object undergoes an increase in wavelength. Whether or not the radiation is visible, "redshift" means an increase in wavelength, equivalent to a decrease in wave frequency and photon energy, in accordance with, respectively, the wave and quantum theories of light.
Doppler Effect
The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.
A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.