Only those that live in the Phoenix metro area break it down. No one else does. For all intents and purposes to anyone not in metro Phoenix area, mesa is Phoenix.
Just like all the greater metro regions of NYC, Boston, LA, Chicago, etc etc
I am from Van Nuys, CA, and grew up in Reseda, CA. They are not the suburbs of Los Angeles, CA. They were annexed into the city and are technically neighborhoods within the city of Los Angeles. Much different than Mesa, AZ, and Phoenix, AZ which are their own individual larger cities. Mesa is one of many nearby suburbs of Phoenix but it is not the same as places where other cities are within another city. My friend lives in White Bear Lake, MN. I can send him mail to his address in White Bear Lake, MN, or in St. Paul, MN and it will get to him. If he sent mail to my address and labeled it Phoenix, AZ - I am not getting it and it would be returned to sender.
As for Paradise Valley, there are technically two. There is a small town (only 15.5 square miles, population of under 13,000) surrounded by Phoenix and Scottsdale and there is a village entirely within the city of Phoenix.
From Wikipedia: The town of Paradise Valley is not to be confused with Paradise Valley Village, an official municipal designation, in northeast Phoenix. For instance, Paradise Valley Community College, Paradise Valley High School, Paradise Valley Hospital, Paradise Valley Mall, and Paradise Valley Golf Course are all several miles north of the town, in Phoenix. The Paradise Valley Unified School District does not serve the town; its boundaries end a few miles north of the border. Residents attend schools in the Scottsdale Unified School District.