Saskatoon is a fruit. Saskatoon is also a city! What is the relationship between them? Is the origin of saskatoon fruit in Saskatoon city?

The city of Saskatoon is named after the berry. There are several different Cree words that refer to the area's prevalence of the sweet violet berry we now call the "Saskatoon Berry," and any one of them could have been translated into English as the word "Saskatoon."

The name Saskatoon (in Cree: sâskwatôn, "Saskatoon" or the locatives: misâskwatôminihk, lit: "at the saskatoon berry", misâskwatôminiskâhk, "at the place of many saskatoon berries", mînisihk "at the berry") comes from the Cree inanimate noun misâskwatômina "saskatoon berries", which refers to the sweet, violet-coloured berry that grows in the area.

There's also a second possible source of the word:

..."the truth appears to be somewhat less dramatic. The area was long-known to the local Cree as a good place to stock up on willow wands for arrow shafts. Thus the name of the place was "Sask-kwa-tan" - roughly, "the place where willows are cut."

https://en.wikipedia.org/wiki/Saskatoon#Etymology