Permits- City or County?

[James Theron Erwin III]

I’ve been reading a lot of old posts about pulling permits and the general consensus is always pull permits when required by the city/county.

My question is this. Which is it? City or county? Or both? I have found the pages for pulling permits for both the city and county I’m in (Tempe and maricopa). Do I need to file with both? Is one more important than the other? Do they likely share info with each other?