I'm from the northeastern USA. I know these objects as "clothespins". According to https://en.wikipedia.org/wiki/Clothespin, "clothespin" (as one word) is the usual word in US English and "clothes peg" (as two words) is the common word in UK English.

the only ones I am familiar with (and I have been doing laundry for a LONG time) is laundry/clothes pegs. I have never heard the other terms used. Although I do have a set of Japanese futon basami which are big clamps used to fix the futon over a balcony railing, or similar. But the average non-Japanese person has probably never seen them.

laundry/clothes pegs, - sure clippers - what? A beard trimmer? Something for shearing sheep? pins - sewing pins, yes, We put a pin in your hip (surgery), drawing pin (thumb tack) clamps - automotive or DIY hobby, large. . New Zealand English. :)