When President Biden stopped by former President Jimmy Carter’s home in Plains, Ga., in April 2021, it was more than just a show of respect from one commander in chief to another. It was the first time in the 40 years since Mr. Carter left the White House that any of his seven successors had visited him in his hometown.

Mr. Carter had a hot-and-cold relationship with the fellow members of the exclusive club of presidents — more cold than hot, in fact. From his re-election defeat in 1980 until his death on Sunday, he was the odd man out, distant from the Republicans and Democrats who followed him and often getting on their nerves because of his outspokenness.

He did not join his fellow presidents on the high-dollar speaking circuit, nor did he team up for many joint humanitarian missions. He was rarely consulted by incumbents except when he forced his way into some issue and made himself hard to ignore. When all of the living presidents gathered to welcome Barack Obama to the White House in 2009, Mr. Carter was the one standing slightly off to the side, removed from his chummy peers physically and metaphorically.

To many of his successors, he was a thorn in their side, always doing his own thing even if it conflicted with official foreign policy. What he considered principled, they considered sanctimonious. While other former presidents generally held their tongues out of deference to the current occupant of the Oval Office, Mr. Carter rarely stood on ceremony.

“I feel that my role as a former president is probably superior to that of other presidents,” he said in 2010.