The Dickinson and the S&W ARE the same guns - Dickinson had their name put on them after S&W stopped importing them
'Dickinson' name was given by the importer Interstate Arms Corporation.
Other posters are confusing Dickinson with the Edinburgh firm of "John Dickson & Son". The John Dickson & Son company introduced the round action shotgun in the 1860s. These are still in production. Genuine Dickson round action sxs presently sell for about $50,000 USD.
(A US firm also used the Dickson name in the USA- American Imports Co. applied the name 'Dickson' to Ugartechea Model 1302 & 1303 shotguns sold under the Falcon Model name. My best guess is the American Imports Co. could use the name in the USA because John Dickson & Son did not bother to Trademark the name 'Dickson' in the USA up to that point. The Falcon Ugartecheas were imported in the late 1960s and early 1970s.)