Staffordshire's southern border has a complicated history! From Wikipedia;

The Counties (Detached Parts) Act 1844 was an Act of Parliament which abolished many of the exclaves of counties in England and Wales. The boundaries of Worcestershire, England have been fluid for over 150 years since the first major changes in 1844.

Worcestershire had an unusually large number of exclaves, which were cut off from the main county and completely surrounded by the nearby counties of Warwickshire, Staffordshire, Gloucestershire, Herefordshire, Shropshire (Detached) and Oxfordshire. The most notable islands were Dudley, Evenlode, Blockley and the area around Shipston-on-Stour.

Herefordshire, Staffordshire, Warwickshire and Shropshire had their own exclaves within the main part of Worcestershire at Rochford, Broome, Clent, Tardebigge (Tutnall and Cobley) and Halesowen. Tardebigge's history is even more colourful, changing hands from Worcestershire to Staffordshire and Warwickshire, before returning to Worcestershire at differing times over the centuries.

A significant boundary change occurred in 1926 when the east of Sedgley was transferred to Worcestershire to allow the construction of the new Priory Estate on land purchased by Dudley County Borough council.

A major reorganisation in the Black Country in 1966, under the recommendation of the Local Government Commission for England led to the creation of an area of contiguous county boroughs. The county borough of Dudley, historically a detached part of Worcestershire, expanded and became associated with Staffordshire instead. This reorganisation led to the administrative county of Staffordshire having a thin protrusion passing between the county boroughs (to the east) and Shropshire, to the west, to form a short border with Worcestershire.

Wolverhampton, Walsall, West Bromwich, and Smethwick were historic Staffordshire towns until local government reorganisation created the West Midlands county in 1974.