The mother parish had a fully qualified vicar (kyrkoherde) while the annex parish was run by a curate (komminister).
In some places the annex parish did not, e.g., issue migration certificates; this was done by the mother parish. An ancestor of mine lived in the (annex) parish of Lerum (Älvsborg county) and his certificate was issued by the mother parish, Stora Lundby.
Usually no migration certificates at all were issued for people moving between the mother parish and the annex parish (or vice versa) since they were regarded as a single administrative unit. This unit consisting of several parishes was called a pastorat, and the vicar was often called a pastor.
In quite a few cases the smaller annex parish is today bigger than the original mother parish. This is the case of e.g. Lerum - Stora Lundby and Kinna - Örby.
Ingela