I would consider the following to comprise the Black Country (the scope of which is still debated!):
Tipton, Dudley, Brierley Hill, Pensnett, Kingswinford, Wordsley, Amblecote, Stourbridge, Lye, Old Hill, Cradley Heath, Rowley Regis and Halesowen (parts of it - some of Halesowen was, and parts still is, quiet rural/ agricultural), Gornal and Sedgley.
Places like Clent, Hagley, Himley definitely not, and I don’t consider Wolverhampton part of the Black Country- others do!
These areas are nearly all in Staffordshire: Dudley is an anomaly, being an island of Worcestershire. A similar anomaly which is not often realised is Amblecote, which was in Staffordshire but was part of the parish of Old Swinford which was in Worcestershire ( Old Swinford also included the parishes of Stourbridge and Lye etc, also in Worcestershire.
The area is characterised by nail making, coal mines (I have seen old maps showing mines in Brierley Hill high Street!, glassmaking etc. Notably the area I have described sits on top of the Staffordshire 10 yard/ 30 foot coal seam.