To kill a teletypewriter (tty) or pseudo terminal slave (pts) user session.

TTY or Teletypewriter;

Directly connected to the system as a keyboard/mouse or a serial connection to the device (i.e. the console on your system).

PTS or pseudo terminal slave;

A terminal device, which is emulated by another program i.e. ssh session.

[source]

Additionally (from above source), to kill a user session, we can do;

killall -u user not so sure this is advisable if the user is root (does it kill off all root processes?)

w to identify the tty/pst

then pkill -9 -t [tty/pst]

OR (preferred)

then ps -ft [tty] the tty is from the output of the w command above.

then kill -9 PID with the PID being from the output from above.