Slimming for the Beach

Does any­one in the great wide world know if mul­ti­ple award-winning coach­builder W. Dwyer of Syd­ney is
related to award win­ning coach­builder John Dwyer of Castle­bar, Co Mayo?
Both were work­ing in the 19th, early 20th cen­turies. I believe the enter­prise in Castle­bar didn’t close till the mid-to-late– 1920s.

This is what the National Library of Aus­tralia has to say about

W. Dwyer (Coach Builder).
Descrip­tion
Joseph Bishop arrived in Mel­bourne dur­ing the gol­drushes, ulti­mately estab­lish­ing a coach build­ing busi­ness at Beech­worth, which was later trans­ferred to Euroa. The fam­ily moved to Mel­bourne in the late 1880s, where one son became the pro­pri­etor of the trade jour­nal ‘The Aus­tralasian Coach­builder and Sad­dler’. The col­lec­tion con­sists of fam­ily pho­tographs and pho­tographs used to illus­trate ‘The Aus­tralasian Coach­builder and Sad­dler’. Pho­to­graph shows a view of a 2 wheeled sin­gle horse sulky. Clearly dis­played on a sign in the photo are the fol­low­ing details: “W. Dwyer, 144 King St New­town. Tel 294 New­town. Coach Builder Syd­ney Wol­lon­gong. First prizes Syd­ney 1898, 1900,01, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12, 13. First Spe­cial & Cham­pion Prizes. Taken all over New South Wales”. This pho­to­graph was most likely orig­i­nally used as an illus­tra­tion for ‘The Aus­tralasian Coach­builder and Sad­dler’.
–
Descrip­tion: National Library of Aus­tralia Pic­ture Aus­tralia

My ques­tion is, were they broth­ers? Or did they have a com­mon ances­tor in the 1798 hero Michael Dwyer, who was trans­ported to Aus­tralia and is buried with his wife Mary Byrne in Sydney.