The term parallelism is usually applied when animals that are related (for example- animals of the same order or of common origin) show the development of similar adaptive features in course of evolution, though they belong to separate species. For example- the present-day crocodiles and some fossil type of crocodile of the Age of Reptiles descended from some primitive reptiles. Both had to pass through distinct evolutionary stages. In course of evolution, they underwent similar changes. The absence of a tail in man, great apes, and gibbon may also be due to parallelism as all of them had common ancestors, who had tails. The tail was lost in course of evolution in separate lines but in a parallel fashion.
The term convergence is usually applied when two species which are not related by common ancestry or so, develop similar characteristics. For example- the hummingbird and hummingmoth show convergence in their flying habits, because they are to follow a common way of searching for nectar in flowers, which is their food. Again, the development of the wings of birds and of bats may be a case of convergence. Another example of convergence is the streamlined shape of whales and fish.
In some cases it is difficult to suggest whether the similarities are due to convergence or due to parallelism. The cause of both is the same. That is, the organisms must develop certain characteristics in order to survive in a similar environment.
In this connection very often we come across two terms- Homology and Analogy. Homology means similarity in structure because of descent from the same ancestral form. For example- the wing of bat and the forelimb of the monkey are homologous because both these have been derived from the same ancestral stock. But the wing of a bat and that of a butterfly are analogous because though both are similar and serve the same purpose, yet they are not descended from a common ancestor. Similarly, the wings of hummingbird and hummingmoth are analogous. Therefore, perhaps we may say that parallelism is homologous evolution and convergence is analogous evolution.