What is the difference between the Houston housing authority and Harris county housing authority? I'm putting in my transfer from port arthur housing to Houston area to be closer to my grandfather who is sick.

There is 2 Housing Authority one which is Houston Housing Authority that do the Houston surrounding area they location is on Fountain View. Harris County Housing Authority is on Husslin Street.

Which one is better for rural areas…

There's only one Housing Authority and its the Harris County Authority. If you are porting directly to Houston you would do the Houston as your county. If you're trying to do any city, you should put Harris County.