The rules are inconsistent. You can be Mayor of Sheffield and an MP at the same time but you can’t be Mayor of Greater Manchester and an MP.
For our American brethren, it's like the difference between being the Mayor of NYC vs the Macy’s Thanksgiving Day Parade King.
There's not much actual difference in the mayoral aspect of the roles - Jarvis was the Mayor of the South Yorkshire Combined Authority, not simply the mayor of Sheffield City Council.