What's the difference between $@ and $* in UNIX?

Please see the bash man page under Special Parameters.

   Special Parameters
       The shell treats several parameters specially.   These  parameters  may
       only be referenced; assignment to them is not allowed.
       *      Expands  to  the positional parameters, starting from one.  When
              the expansion occurs within double quotes, it expands to a  sin‐
              gle word with the value of each parameter separated by the first
              character of the IFS special variable.  That is, "$*" is equiva‐
              lent to "$1c$2c...", where c is the first character of the value
              of the IFS variable.  If IFS is unset, the parameters are  sepa‐
              rated  by  spaces.   If  IFS  is null, the parameters are joined
              without intervening separators.
       @      Expands to the positional parameters, starting from  one.   When
              the  expansion  occurs  within  double  quotes,  each  parameter
              expands to a separate word.  That is, "$@" is equivalent to "$1"
              "$2"  ...   If the double-quoted expansion occurs within a word,
              the expansion of the first parameter is joined with  the  begin‐
              ning  part  of  the original word, and the expansion of the last
              parameter is joined with the last part  of  the  original  word.
              When  there  are no positional parameters, "$@" and $@ expand to
              nothing (i.e., they are removed).

One difference is in how they handle the IFS variable on output.

#!/bin/sh
echo "unquoted asterisk " $*
echo "quoted asterisk $*"
echo "unquoted at " $@
echo "quoted at $@"
IFS="X"
echo "IFS is now $IFS"
echo "unquoted asterisk " $*
echo "quoted asterisk $*"
echo "unquoted at " $@
echo "quoted at $@"

If you run this like this: ./demo abc def ghi, you get this output:

unquoted asterisk abc def ghi
quoted asterisk abc def ghi
unquoted at abc def ghi
quoted at abc def ghi
IFS is now X
unquoted asterisk abc def ghi
quoted asterisk abcXdefXghi
unquoted at abc def ghi
quoted at abc def ghi

Notice that (only) the "quoted asterisk" line shows an X between each "word" after IFS is changed to "X". If the value of IFS contains multiple characters, only the first character is used for this purpose.

This feature can also be used for other arrays:

$ array=(123 456 789)
$ saveIFS=$IFS; IFS="|"
$ echo "${array[*]}"
123|456|789
$ IFS=$saveIFS

for i in "$@"
do
    echo $i  # loop $# times
done

for i in "$*"
do
    echo $i  # loop 1 times
done

It's safer to use "$@" instead of $*. When you use multiword strings as arguments to a shell script, it's only "$@" that interprets each quoted argument as a separate argument.

As the output above suggests, if you use $*, the shell makes a wrong count of the arguments.