The average size of the board of a company in the S&P 500 is 10.8 directors. However, only 43% of CEOs serve on any outside boards. The implication is that the vast majority of board directors are not CEOs of large companies.
It's more appropriate to think of this as a class of "the pool of people who might become CEO". It's CEO, CTO, CIO, board members who also have their compensation decided by similar mechanisms, retired CXOs.
Let's take Intel as an example - Retired CEO of medtronic, CEO of Intel, Sequoia, Senior position at Square, former CEO of a foundation, Professor, EVP and CFO Boeing, former CEO of HP, CEO of EA, Darwin Capital.
So in total, of a board of 10, 6 of them are current or former CXOs, 1 is a professor, 2 are VCs and 1 is a senior CXO style position. Yet most of those wouldn't be counted as "CEOs" because they're "retired".
Data from https://www.briefinggovernance.com/2016/12/board-composition...