John Smith and Samuel Smith are often said to have been brothers. John Smith did have a brother named Samuel, but the Samuel Smith who established the brewing business of that name was the son of that Samuel.
In short: the first Samuel Smith was a tanner based in Leeds, who in 1847 set his second son John up in a struggling brewing business in Tadcaster. John Smith turned the business around, and on his death it passed to his two brothers, William and Samuel. Samuel Smith Jr. had no experience of the brewing business, having taken over the tanning business from Samuel Sr. William therefore bought out Samuel's share of the business, and ran it with his nephews Henry and Frank Riley, the sons of the three brothers' only sister, Sarah Riley.
William Smith also began the building of a new brewery on an adjacent site. On William's death, the new brewery passed to the Rileys (who changed their name to Riley–Smith as a condition of their inheritance) and the old brewery passed to Samuel's son, Samuel III, who used it to set up his own brewing business. Henry and Frank Riley, and Samuel Smith III, were all nephews of John Smith.
For more detail, please refer to my separate note, which is attached to the relevant entry on the UK Towns & Cities page..
© Haydn Thompson 2019