> tst1 a b "c d"
>
> tst2 $*  <-- this would expand above to 4 args instead of 3.
> tst2 "$*" <-- this would expand above to 1 arg instead of 3.
>
> How do I get the original three args?

tst2 "$@"

is equivalent to using

tst2 "$1" "$2" "$3"

In summary, for original example:

 $@     4 args
 $*     4 args
 "$*"    1 arg
 "$@"    3 args!

Beside, when there are no positional parameters, “$@” and $@ expand to nothing (i.e., they are removed). No need to play the trick ${1+"$@"}!