What I learned is that Circle K was established in 1979 as an alliance between a Japanese company (Yunii Kabushiki Kaisha, a supermarkets chain) and an American corporation (Circle K), having the first store opened in Nagoya the next year. Sunkus Co. was a different company, established in 1980 by Nagasakiya Co., with the first store opened in Sendai. Both were successful companies and grew separately until 1998, when they formed an alliance, creating the Circle K Sunkus Co. But the two brands remain distinct, so that's why you will meet in Japan similar konbini, branded either with the Sunkus or with the Circle K.
Photographed here is the konbini that raised my curiosity: this Sunkus from Ueno, one of my most frequent stops for a couple of years...
EXIF info:
Nikon D90
Lens: VR 18-55mm F/3.5-5.6G
Focal Length: 28mm
Aperture: F/5.6
Shutter Speed: 1/600s
ISO Sensitivity: ISO 200