From the Smart matching in detail section in perlsyn:
The smart match operator short-circuits whenever possible.
Does ~~ have anything in common with short circuit operators (&&, ||, etc.) ?
The meaning of short-circuiting here is that evaluation will stop as soon as the boolean outcome is established.
perl -E "@x=qw/a b c d/; for (qw/b w/) { say qq($_ - ), $_ ~~ @x ? q(ja) : q(nein) }"
For the input b, Perl won't look at the elements following b in @x. The grep built-in, on the other hand, to which the document you quote makes reference, will process the entire list even though all that's needed might be a boolean.
perl -E "@x=qw/a b c/; for (qw/b d/) { say qq($_ - ), scalar grep $_, @x ? q(ja) : q(nein) }"