a. Functional group:
A functional group is a group of atoms in a molecule that will define the properties of that molecule regadless of the other atoms in the molecule.
These group of atoms are responsible for the properties of the molecule.
For example: these are three different functional groups.
b. Homologous series:
The homologoues series are a group of compounds in which the difference between the members is a simple structural unit. They are carbon compounds that contain different number of carbon atoms but they have the same functional group.
Since they have the same basic structure and the same functional group the chemical properties are similar inside the same homologoues serie.
For example: These are two different homologous series.