I have also found several Caseys that are related to my GGF Michael, but little info about how they are connected. Michael's father was Michael and he had a son Michael, but he also lived with another Michael Casey, who I presume was a cousin; the cousin was born in Limerick in 1851 and entered the US through New York, but lived with my Michael in Boston for several years before disappearing. They were both naturalized US citizens on the same day (10/31/1876) and appear on consecutive pages in the records.
Also naturalized on the same day is William Casey and the witnesses for his naturalization were the same as my Michael's (Thomas O'Brien, the maiden name of Michael's mother, and Ed Davine/Devine, apparently Michael's landlord). According to the record, William was born 3/5/1851 in Tipperary and arrived in Boston in 1866. The witness at Michael Casey's wedding was William Casey (probably the same one), and Michael subsequently had a child he named William.
Thomas Casey was the godparent for the birth of one of Michael's children, as were Patrick Casey and Catherine Casey. I have no information on how they may be related, but it is very likely that they are.
In addition, there was a John Casey (b. Ireland), married to Ellen, who had a son named William in 1870 in Boston. John died and Ellen later boarded both of the Michaels I was tracking at one time, and many of the Caseys I found worked in the printing industry in Boston. Ellen's son William later became the superintendent of printing for the city of Boston, and his son William became a Jesuit priest and served in Iraq, among other places, before dying in the early 1990s. My father remembers being taken to the first mass of a family priest in the 1930s, and it was very likely William Casey he saw; there is a strong indication that we are related to this branch - through John Casey - as well.