The main difference between 2x2x2 block and cross is that block has a corner piece, which has 3 different orientations. We understand edges from cross, but how to freely flip that corner around is new material to me.
Cube Explorer will tell me God's algorithm and these "pop quizzes" are just interesting standalone puzzle challenges for the amateur block-builder to toy with and dissect...or destroy, depending on their skill level. For me, it's all dazzling...
R U' R U R' -- Permute FU to RU with FRU & FR already solved (makes 1x2x2 panel on R)
R U' R' U R' -- Permute RU to FU with FRU & FR already solved (makes panel on F)
One the one hand, these are actual cases you could setup and gogogo. But I think it's even more interesting to study how they work. God was so clever here...
* The number 4 in the diagram is a hint for the 4th block piece