A rule clearly and specifically states what you are permitted or not permitted to do, while a policy provides general guidelines for you to make decisions about what you do or do not do. I do not think of these as "small" differences, though, since they are completely different approaches to regulating employee behavior. Let me provide a few examples.
A company could have a policy stating that sexual harassment will not be tolerated in the workplace. A rule, though, would state that employees are not permitted to date one another or that people are not permitted to send emails at work that contains sexual content. In the one case, the policy statement guides people's decisions about what they should or should not do, while in the others, it is clear what the employee is not permitted to do.
A company could have a policy promoting social responsibility, saying "This company is committed to being a socially responsible member of the community." A rule on the same subject might be that employees must use 10% of their work hours on a social responsibility project.
You can see that the approach is quite different, since a policy promotes an ideal without saying anything about how to achieve that ideal, but a rule explicitly governs employee behavior. Policies are a form of guidance, while rules tell us what we can and cannot do. Most workplaces find a need to have both.