In general usage, specialty and speciality are very closely related and often interchangeable. English reference books say various things about them, but in general writers tend to treat them as if they’re the same word. Specialty is more common in American, Canadian, and Australian English (which is surprising, because Australian English usually follows British), and it’s usually a noun meaning something in which a person or business specializes. Speciality is more common in British English, and it’s often an adjective (as in the phrases specialty store and specialty products).
Mr Walgren said that, at the time of Jackson’s death, Dr Murray was not certified in any medical speciality. [Telegraph]
One of the guinea pigs for Nest has been a small speciality chemical manufacturer from Preston. [BBC]
Our host, Calogero, duly piled the table high with varieties of another local speciality: fresh goat’s cheese. [Guardian]
Specialty (everywhere else)
His specialty is “generational accounting,” which was the issue that kicked off the TV debate. [Star-Ledger]
Craft and specialty beers are keeping the domestic beer industry afloat. [Vancouver Sun]
Find a pub with tables outside and sit down to watch the world go by over a stein of beer or an apfelwein, a local specialty. [Sydney Morning Herald]