The link between the two monarchs goes back to Queen Victoria, who was the great-great-grandmother to Queen Elizabeth (through her father, King George VI) and great-great-grandmother of King Carl XVI Gustaf through both his mother and father through two of Victoria’s sons, Prince Arthur, Duke of Connaught and Strathearn and Prince Leopold, Duke of Albany.
Queen Victoria’s eldest son, King Edward VII, had King George V (Elizabeth’s grandfather) with his wife, Queen Alexandra. King George V was the father of Elizabeth’s father, King George VI, with his wife Queen Mary.
Queen Victoria’s son, Prince Arthur, married Princess Louise Margaret of Prussia and had Princess Margaret, who would become Crown Princess of Sweden after marrying the future King Gustaf VI Adolf (King Carl XVI Gustaf’s grandfather). Their son was Prince Gustaf Adolf, Duke of Västerbotten – the current Swedish King’s father who died when his son was just nine months old.
Another of Victoria’s sons, Prince Leopold, Duke of Albany, married Princess Helena Friederike of Waldeck and Pyrmont; together, they had two children, including the future Charles Edward, Duke of Saxe-Coburg and Gotha. Charles Edward was the father of Princess Sibylla – King Carl XVI Gustaf’s mother.
Thus, Elizabeth and Carl Gustaf were third cousins, and Sweden’s royals are in the British line of succession. The Swedish royals rank in the 200s in the British line of succession.
Queen Victoria, being “Europe’s grandmother”, married her children off into the other royal families of Europe, solidifying her link to each of the royal houses.
