They mean exactly the same thing: a particular skill, focus, or signature product. Specialty is the American spelling, while speciality is the standard British one. In UK writing, stick with speciality; in US writing, use specialty.
The core difference
Specialty and speciality are the same word, split only by American versus British spelling.
- specialty — the American spelling: His specialty is corporate tax law.
- speciality — the standard British spelling of the same word: Paella is a speciality of the Valencia region.
How to tell them apart
There is no meaning difference to memorise here, only a spelling one. Both words cover the same two ideas: a subject or skill someone focuses on, and a product a place is known for. The extra i in speciality is the giveaway for British English, in the same family as pairs like colour and color.
The mix-up usually shows up in menus, CVs, and professional bios, where writers copy a spelling from an American source without adjusting it for a British audience, or the other way round.