The difference appears when the special parameters are quoted. Let me illustrate the differences:
$ set -- "arg 1" "arg 2" "arg 3"
$ for word in $*; do echo "$word"; done
arg
1
arg
2
arg
3
$ for word in $@; do echo "$word"; done
arg
1
arg
2
arg
3
$ for word in "$*"; do echo "$word"; done
arg 1 arg 2 arg 3
$ for word in "$@"; do echo "$word"; done
arg 1
arg 2
arg 3
one further example on the importance of quoting: note there are 2 spaces between "arg" and the number, but if I fail to quote $word:
$ for word in "$@"; do echo $word; done
arg 1
arg 2
arg 3
and in bash, "$@"
is the "default" list to iterate over:
$ for word; do echo "$word"; done
arg 1
arg 2
arg 3