Punctuated equilibrium : It is a theory in evolutionary biology which proposes that once a species appear in the fossil record they become stable, showing little net evolutionary change for most of their geological history.
You are right. Punctuated equilibrium suggests that species do not change for long periods of geological history and thus, the fossils look the same. It may accumulate mutations, which are recessive and do not affect the phenotype. However, due to the action of some factors, such as catastrophes or significant changes in radioactive background, or changes in temperature, accumulation of the critical number of mutations, the phenotypical changes may appear in the organisms, which results in formation of new species. Then, fossil records show the appearance of the new species at some time of history.