So printf(1) is the man page for the /usr/bin/printf command, while printf(3) is the man page for the libc printf() function.
Alternatively, readdir(2) is the man page for the readdir syscall, while readdir(3) is the man page for the libc wrapper, which no longer actually calls readdir(2). See also syslog(2) and syslog(3).
Or, time(1) is the man page for /usr/bin/time to time how long commands take. time(2) is the syscall to return the number of seconds since the epoch. And time(7) gives you an overview of time and timers on the system.