Huron, I think you are mostly right about the Patch, but here is an example of its wide misuse, you will see the same thing in books.

Here the Wiki author on the 42 Gang entry is saying it’s where Cabrini was:

The Forty-Two Gang started in 1925, with twenty-four members (some as young as nine years). The boys supposedly named their gang after Ali Baba and the Forty Thieves, claiming they were one better than their fictional namesakes. The gang came from a Chicago neighborhood known alternatively as "the Patch," "Little Sicily," or "Little Hell" and was on the city's Near North Side. The neighborhood was later razed to accommodate Cabrini Green.

In the book “JFK and Sam” the author says it is the Little Italy area on South Aberdeen:

Gilormo Giancana was born on the West side of Chicago in 1908. Baptized Momo Salvatore Giancana, he was known as “Sam.” He lived with his parents—Antonino Giancana, a Sicilian immigrant grocer, and Antonia DiSimone—in a tenement (a housing structure for the poor) on South Aberdeen Street in a neighborhood referred to as “The Patch.”

Here’s a mob site saying it’s around Grand and Ogden:

Frank Cullotta born Dec. 14, 1938 on Grand and Ogden in the area called The Patch in Chicago IL.

And here’s a reference to Tony Spilotro in line with the far smaller Western/Washtenaw boundary:

“Unlike most Italian immigrants who settled in "The Patch," (located around Grand and Western Avenues, the Spilotros lived at 2152 North Melvina Avenue.”