Either way, the ask was for a difference in www.example.com vs example.com. Not a difference in www.pool.example.com vs pool.example.com. In the latter case, the different subdomains will still be shown (AFAIK).
>Even if you ultimately end up at the same site through redirects, you're clearly not going to the same site initially.
Which is nothing that an end user is going to care about and doesn't provide an example to the asked question.