Allopatric species are the species which occupy a different geographical area. For example, the species of frogs which are found in India and in Srilanka. The two land areas are separated by the Gulf of Munnar. So, there is the difference in the species of the frogs found in these two regions. There is a natural mutation in these organisms which allows them to adapt to the environment. They cannot interbreed due to the geographical barriers.
Whereas sympatric species are the closely related species living together in one common locality yet maintain their species identity. For example, Rana hexadactyla, Rana tigrina and Rana cyanophlictis are the different species of frogs which are living together in a pond. There are differences in the species and they maintain the systems like different ploidy levels and do not interbreed with the other species.