How do gradualism and punctuated equilibrium differ? How are they similar?

Hint: Gradualism and punctuated equilibrium are related to the evolution of species over a period of time. The evolution in the species could be either sudden due to mutation or gradual due to slow changes occurring in it.

Complete answer:
There are two ways for evolution of a species- gradualism and punctuated equilibrium. Species can evolve either by one of these methods or by both. Species that have a shorter evolution generally follow a punctuated equilibrium path whereas the species with longer evolution evolve mostly by gradualism.
In gradualism the selection and variation occurs more gradually over a shorter period of time and it is hard to notice. Over a long time, very gradually the population changes. So, it is constant, slow and consistent.
In case of punctuated equilibrium the changes come in spurts that is initially there is a period of small change which is followed by a few huge changes. This often occurs through mutation in the genes of an organism. Mutation in this case are random changes in the genetic material of the organism that are not inherited from the previous generation. These mutations prove helpful to the individual in their environment so the proportion of individuals in the population that have the mutation and the proportion that do not have the mutation changes a lot over a very short time period. There is a sudden change in the species over a few generations which settles down again to a period of small changes.

Note: Both refer to organisms' evolution over time. Gradualism, however, claims that evolution has slowly occurred over a long period of time. Punctuated equilibrium occurs when abrupt alteration breaks periods of apparent stasis.