The Poor Law Amendment Act 1834 and its administration entailed the creation of entirely new administrative areas throughout the United Kingdom: groups of parishes known as Poor Law Unions or simply Unions.
(Parish here = civil parish, defined as "area[s] for which a poor rate is or can be assessed" in mid-19th century legislation, as for example the Poor Law Amendment Act 1866; the thing is of course older than the term.)
These groupings were based on geographical and demographic practicalities and took little account of most previous administrative arrangements, even cutting across county boundaries if necessary.
Note below, for example, Bourton and Silton, which although in Dorset, were for decades in the Wiltshire Union of Mere, and thus the Poor Law County of Wiltshire; the Somerset parishes in Sherborne Union, and thus in the Poor Law County of Dorset; and Lyme Regis, in Axminster Union and the Poor Law County of Devon.
In Dorset, however, the 1834 Unions were closely related to the pre-existing divisions (a unit developed principally for tax purposes), updated as recently as 1830 in a local Act of Parliament.