As a response to the COVID-19 pandemic, social-distancing measures have been implemented worldwide, including school closures. Previous studies indicated that children's relational social cohesion with family (RSC-Fa) and friends (RSC-Fr) may have decreased during the pandemic, but some children described that positive experiences were gained from the confinement measures of social distancing. Mostly, these studies are qualitative or capture a single country and have an exploratory character. Using data collected in 2021 of more than 20,000 children primarily aged 9–13 years as part of the International Children's Worlds COVID-19 Supplement Survey from 18 countries (Germany, Turkey, Bangladesh, Italy, Albania, Romania, Chile, Wales, Taiwan, Belgium, Algeria, Israel, Russia, South Korea, Indonesia, Estonia, Finland, and Spain), this study aimed to examine how the COVID-19 pandemic has affected children's RSC-Fa and RSC-Fr and explore the role of relational factors. RSC-Fa and RSC-Fr are measured through satisfaction in relationships with family members and friends before and during the COVID-19 pandemic, respectively. We employed descriptive statistics, cluster analysis, and multinomial logistic regression analysis. Our analyses confirmed the decrease in RSC-Fa and RSC-Fr, with a noticeably bigger decrease in RSC-Fr. Five profiles of change in RSC emerged: (1) gainers in both RSC; (2) gainers in RSC-Fa and decliners in RSC-Fr; (3) no change in either RSC; (4) decliners in RSC-Fa and gainers in RSC-Fr; and (5) decliners in both RSC. The quantity and quality of children's relationships differ by their profiles of change in RSC. For example, it was significantly more likely that “decliners in both RSC” had to be at home all day because of COVID-19 than “gainers in both RSC” or “no changers.” Mainly, the quantity of relationship factors, and among different quality factors, only autonomy perceptions, help to explain the children belonging to the “gainers in both RSC” profile compared to the “no changers.” Meanwhile, almost all the quantity and quality of relationships factors help to explain children's belonging to the “decliners in both RSC” profile compared to “no changers.” In conclusion, our study confirmed the importance of keeping schools open to protect the RSC of children.