Clipping one wing is an "old-school" method. Some people still do it, but it's generally considered a bad idea. The idea is that they don't get distance, they don't glide that 4-6 feet like they do with both wings clipped ,they just kind of go straight down. Same with the "macaw" or "beauty" cuts where the 2 primary flights are left on but all the rest are clipped, so that with the wings closed they look like they have full wings. But that just leaves 2 stray feathers to get caught on things, broken, etc. It really boils down to every groomer/vet having their own preference and philosophy and views on safety. I still see vets who clip the coverts, who clip almost the whole wing, who clip too much, too little... but that's all to my personal standard which is to clip just the first 2-4 primaries up to the coverts, sometimes just behind so it leaves a nice clean line for fussy owners who want the bird to "look pretty" lol
Back in the day, people used to pinion the birds too - which means they pulled out
the flight feathers repeatedly until they no longer grew back in. I've only met a few birds which had this, generally wild caught older birds but it's very sad
I had an owner who was elderly who had always had it done with his bird (40 year old amazon) ask us to do it until we compared it to pulling out fingernails until they stopped growing... he never realized it hurt the bird, he was always told it was the right thing to do and his vet did it for him until the vet retired and closed shop. I felt so bad for both him and his bird, I'd never seen an owner turn so pale and look so stricken with guilt so quickly.