Hamburgers get beef fat; sausage gets pork fat, here.
YMMV
For sausage we use straight pork butts for making breakfast and Italian sausages. Buy them on sale for $.99 a pound and they are just about the perfect fat/lean ratio at roughly 30/70. Add the seasonings and you are good to go.
I do the same w shoulders. But, I don’t think the shoulders I get are 30%. Really don’t leave grease in the skillet. Sausage, IMO, needs the fat.
Pork butts come from the shoulders. Why they call them butts is beyond me.
Because they used to salt pack them in wooden barrels, called Butts.
Back in wood ships and sails days.
Common explanation, but apparently a debatable one.
Skepticism of the "Boston Butt"
The New York Times and other reputable publications have repeated this story, but common sense should make us skeptical. Can you think of any other food named for its shipping container name?
There are plenty of historical problems with this explanation, too. For starters, Virginia and North Carolina, not New England, were the centers of the pork trade in the 18th century until eclipsed by Cincinnati in the 1830s and then by Chicago. I have searched high and low but cannot find a single printed use of the term "Boston butt" in the colonial era or even before the Civil War.
Other Geographically-Names Cuts
The term originated in the late 19th century, as railroads transformed the commercial meat packing industry from regional to national. Butchers in different parts of the country had slightly different ways of carving up pigs and cows. Other states and cities lent their names to various cuts as national packers standardized butchering. Thus we have New York Strip steaks and St. Louis-style ribs—another favorite of Southern barbecue cooks.
The pork shoulder originally had several other geographically-named cuts. In the meatpacking trade, the Kansas City Sun reported in 1892, "careful requirements are formulated for standard sweet pickled hams and shoulders, New York shoulders, Boston shoulders, California hams, skinned hams, pickled bellies, etc."
According to agriculture journals and meat cutter manuals from the early 20th century, New York shoulders had the shank "cut off above the knee, trimmed close and smooth, and square at the butt." A "California ham" was not ham at all. It was "well-rounded at the butt, and trimmed as near to the shape of a ham as possible." This latter cut was also known as the "picnic" (for reasons I've been unable to discover), and that term is now the standard for the lower part of the pork shoulder.
Agricultural Terminology
As the use of "butt" in these agricultural manuals suggests, the name of the Boston-style cut had nothing to do with shipping containers. Consider the butt of a rifle or a cigar butt. Either crafty Bostonians were putting all sorts of things in barrels and shipping them south, or "butt" was simply a generic term for, as Merriam-Webster phrases it, "the large or thicker end part of something"—the pork shoulder, in this case.
Boston didn't have a monopoly on butts, either. The 1912 Bulletin of the Agricultural Experiment Station of the University of Illinois at Urbana-Champaign observed, "Milwaukee style butts are the same as Boston butts with the neck bone and rib left on." My research even turned up a passing mention of a "New Orleans cut" of pork shoulder in 1911, but that one never became popular, which is a shame.
https://www.southernliving.com/food/bbq/why-is-it-called-boston-butt