It gets complicated.
Douglas straddles the two parishes of Braddan and Onchan, the majority of the town being physically in the parish of Onchan.

For church purposes, Braddan is the Parish Church of Douglas.
The other churches such as St George, St Matthew, St Barnabas, St Thomas were physically in Onchan but were under Braddan.

As a result the terms Braddan and Douglas are often found interchangably.