I see no justification for there having to be two types of atheism as this is inconsistent with the other positions [theism and agnosticism]
When it comes to branching [types of], these can be shown as sub-sets...so subsets of theism are religions {which includes all forms of Gnosticism) and everything to do with having some type of leaning towards support for the existence of "GOD" [including my leaning toward the idea of a Cosmic Mind]
So the 'forms' of atheism [ weak and strong] should be observed as types of atheism [subsets] and agnosticism should not be regarded as branching from atheism as a 'type' [usually said to being 'weak'] but rather, should be regarded as distinct from either theism or atheism.
Graphically, it would look something like;