They do the same thing, it's all about operator precedence. || has higher precedence than or, and other things in between. The perlop manpage has about everything you need to know. To steal an example from perlop, the following:
    unlink "alpha", "beta", "gamma" or gripe(), next LINE;
works like:
    unlink("alpha", "beta", "gamma") or (gripe(), next LINE);
but it would break using ||, because it would work like:
    unlink("alpha", "beta", ("gamma" || gripe()), next LINE;