I think Great Chatwell is right on the border of both counties
Yes, and the border shifted at one stage (not sure of the dates), so it is listed sometimes as Staffordshire and sometimes as Shropshire. However, Great Chatwell was part of the Blymhill parish, and I was assuming the records would be in Staffordshire.
Thanks for looking up those entries in the IGI. I was unsure whether the marriage entry was theirs (despite being a good match), because I was expecting they would have married in either Blymhill or Brewood (I don't know of any connection to Wolverhampton central). Still, it is not too many miles away. In the 1871 census, Thomas was living in Great Chatwell, and Catherine's mother and daughter Lucy (not from the marriage to Thomas) were living at Bishop's Wood.
I don't think the Selattyn and Saint Martins entries are for the same Thomas, because they are too far away from Great Chatwell (and Thomas Price is a common name).
Catherine was still living at Blymhill in the 1920s (I have a picture of her taken at Blymhill common).