Derbyshire is an English Shire or County.The major city and county seat of Derbyshire is, (or was -- they've recently changed everything over there) the city of Derby.Bakewell is a town and a parish in Derbyshire to the west of Derby which has a parish church, All Saints.
It is not the same but Derbyshire is somewhat analogous to Tennessee, Derby to Nashville, and Bakewell Parish to DeKalb County.If someone was listed as being from “Derby” they could have been from anywhere in Derbyshire.
But there are scores of other parishes in Derbyshire.Bakewell registers have about 25-30 Cantrells in the 17th-18th Century period and Ashover has about 30-40.So I am assuming there are at least hundreds of Cantrells in the Derbyshire Parish records, if not thousands.
As these records are indexed and digitized we may connect Richard and Joseph of Phila. to one of the Parish records.Have worked a lot with local records here, and I was surprised at the completeness of the Bakewell Registers.
BTW, Lichfield is NOT in Derbyshire, but it was the seat of the Ecclesiatical Court that oversaw probate in Derbyshire during this time period, and Richard's (d 1638) probate records are there.(I am not entirely clear on this Court’s jurisdiction or structure.)