The reason why we see resonances at different chemical shifts for functional groups is that the carbons bonded in these groups are in different chemical environments.
The chemical environment of a carbon atom is affected by the surrounding atoms. Electronegativity, pi electrons, inductive effects and large electron density are examples of the factors that contribute towards the varying chemical shifts.
The number of chemical environments can be identified from the number of peaks in the spectrum.
Figure 1: Carbon NMR spectrum of Ethanol
There are two peaks on the spectrum indicating two chemical environments. The aliphatic carbon and the alcohol group carbon.
Remember that the number of peaks is not the same as identifying the number of carbon molecules. Instead, the peak height may give an indication if there is more than one carbon atom in that chemical environment.
These carbons are referred to as Chemically equivalent