controlling terminal - to have and have not

[Jan Stary]

This is how ps(1) differentiates between displaying
processes that have a terminal and those that have not:

        -a Display information about processes
           for all users with controlling terminals.

        -x Display information about processes
           without controlling terminals.

Strangely, some processes appear in both listings:

  $ ps -a | grep man 
  22867 p6  Ip       0:00.02 man ps
  82326 p6  I+p      0:00.02 less -T /tmp/man.TkUznrbk0K /tmp/man.qGVXE5xsvJ
  43736 p7  R+p/3    0:00.00 grep man

  $ ps -x | grep man 
  22867 p6  Ip       0:00.02 man ps
  82326 p6  I+p      0:00.02 less -T /tmp/man.TkUznrbk0K /tmp/man.qGVXE5xsvJ
  50867 p7  R+p/2    0:00.05 grep man

Is this intended? Am I missing something obvious?
Or does the wording mean "users with controlling terminals"?

Jan