The difference (in my opinion) would be between

eval 1/0 # compile-time error
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and

my $d= 0;
eval 1/$d;
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Maybe that would be a solution to discern between compile- and runtime-errors - wrap the code in question in a subroutine. If the code compiles, then we don't have a compile-time error:

my $code;
my $ok= eval sprintf q{
    $code= sub {
        %s
    };
    1
}, $string;

if(! $ok) {
    my $err= $@;
    warn "Compile error on $string: $err";
};

$ok= eval {
    $code->();
    1;
};
if( ! $ok) {
    my $err= $@;
    warn "Runtime error on $string: $err";
};
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Update: Upon testing, I now realize that 1/0 does not generate a compile-time error. But at least, that way one could find out whether there is a compile-time error or a runtime error.