Difference in bash's $@ and $* and how it is expanded

I keep forgetting about this and I'm always confused what is happening but it is not that difficult. Example:

$ function measurement_add() {     python -c "import sys; print sys.argv[1:]" $@; }
$ measurement_add "Hello world" 1
['Hello', 'world', '1']
$ function measurement_add() {     python -c "import sys; print sys.argv[1:]" $*; }
$ measurement_add "Hello world" 1
['Hello', 'world', '1']
$ function measurement_add() {     python -c "import sys; print sys.argv[1:]" "$@"; }
$ measurement_add "Hello world" 1
['Hello world', '1']
$ function measurement_add() {     python -c "import sys; print sys.argv[1:]" "$*"; }
$ measurement_add "Hello world" 1
['Hello world 1']

Looking into man bash into Special Parameters section:

       *      Expands to the positional parameters, starting from  one.   When
              the  expansion  is  not  within  double  quotes, each positional
              parameter expands to a separate word.  In contexts where  it  is
              performed, those words are subject to further word splitting and
              pathname expansion.  When the  expansion  occurs  within  double
              quotes,  it  expands  to  a  single  word with the value of each
              parameter separated by the first character of  the  IFS  special
              variable.   That  is, "$*" is equivalent to "$1c$2c...", where c
              is the first character of the value of the IFS variable.  If IFS
              is  unset,  the  parameters  are separated by spaces.  If IFS is
              null, the parameters are joined without intervening separators.
       @      Expands to the positional parameters, starting from  one.   When
              the  expansion  occurs  within  double  quotes,  each  parameter
              expands to a separate word.  That is, "$@" 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).