The following command sends the default TERM (termination) signal:
killall Finder The available signals for stopping a program, in order of niceness are TERM, QUIT, KILL.
killall -QUIT Finder
killall -KILL Finder If the TERM fails to terminate a program, the next step would be to try QUIT. If the program does not respond to QUIT either, then as a last resort the KILL signal should be used. KILL cannot be ignored by a program, the operating system will terminate it immediately. TERM and QUIT are designed to give a process the chance to clean up before exiting, whereas KILL will stop the process whatever it may be doing.
You can see a list of all signals (not all are for killing) with kill -l. A summary of the ones for killing a program are:
HUP Hangup - stop running. Sent when you log out or disconnect a modem
INT Interrupt - stop running. Sent when you type CTRL-c
QUIT Quit - stop running (and dump core). Sent when you type CTRL-\
KILL Kill - stop unconditionally and immediately; "emergency kill."
TERM Terminate - terminate gracefully, if possible
STOP Stop unconditionally and immediately; continue with CONT
CONT Continue - continue executing after STOP or TSTP
The kill command is named because of the nature of the default TERM signal, but in general it's used to send a variety of signals to programs. There are summaries on the man pages man kill and man killall but they're not very useful to learn from. Better descriptions can be found by googling something like "unix signals kill term quit".
Having said all that, if I want to re-launch my Finder while it is still responding, I like to use ⌥ + "click & hold" on the Finder dock icon, then select relaunch which is bottom on the list.