I can then diapers when I'm talking with my wife. With healthcare people, it varies - I'll often call them incontinence briefs, because many doctors and nurses are trained not to call them diapers due to that potentially being considered a demeaning or embarrassing term by some patients.
Some non-urological folks get confused by the term "incontinence brief," so sometimes I have to clarify. At my dermatology appointment last month, the nurse told me to take off all my clothes except my underwear and put on a gown. I got her that I was wearing an incontinence brief, and asked if I should leave that on or take it off, and she gave me a blank look. As soon as I told her it was an adult diaper, she was able to answer the question. (She had me keep it on, and the doctor had me untape it and pull it down to do the skin exam in that area.)
At the end of the day, I believe the point of language is to communicate clearly. I work hard not to be ashamed of my incontinence (sometimes I even succeed), and I don't think using euphemisms is necessary. I don't buy the idea that calling them diapers or nappies will reduce the stigma, but I do like to be precise with my words.