I would also agree that there are differences between anagenesis and cladogenesis. However, the genetic mechanisms are the same in both cases. Where they differ is in the mode of speciation.
In both cases, the differences between species is due to mutations. With anagenesis, there is a single lineage that accumulates mutations and keeps those mutations within the species, and over time the accumulation is enough that the descendant population is noticeably different from the ancestral population. With cladogenesis, mutations accumulate in the population which results in genetic variation. That population is shattered into many subpopulations where different variants become fixed in each subpopulation. In both cases, the genetic and phenotypic differences between populations are due to the accumulation of mutations, either over time or in the ancestral population that spawned many new species. Where cladogenesis and anagenesis differ is in the mechanism of speciation and large scale effects of selection.
Actually, that is part of the question.