The usual problem of graph partitioning is to split a graph (or a mesh) into two partitions.
According to its Github repository's README file, KaHyPar supports both recursive bisection and direct k-way partitioning.
I suppose that recursive bisection is just a recursive application on the partitions of a graph produced by a partition algorithm which produces two partitions, whereas direct k-way partitioning may not use recursion, but it's simply an algorithm which tries to divide the graph directly into the desired number of partitions.
If this is correct, are there any other differences between the two approaches? If not, what is the difference between the two approaches? By the way, is the terminology consistent throughout the literature?