What are the differences between word puzzles and homophonic words in Xiehouyu?

Xiehouyu anagrams and homophonic word jokes

For example:

The bag in the air -------- pretending to be crazy. (pretend to be cool).

Song Jiang’s military advisor is useless. (Wu Yong).

The old woman went to the henhouse----Idiot. (Bendan).

The straw hat seller throws his pole------be careful. (leave the rope).

My brother is not at home----------Don't come. (Sister-in-law comes).

My nephew is lighting a lantern----------as usual. (Uncle Zhao).

The rain hits the yellow plum head----------unlucky. (fallen plum).

Half a tael of cotton------------No need to discuss. (no bullet required).