Facebook allows for 2 networking tools:

1. Creating/ joining a Facebook group;
2. Creating/ joining a Facebook fan page.

While the major differences become evident only after you try out them first. The following is what I found:

First and foremost the 2 major differences include:

1. Unlike groups, fan pages are visible to unregistered people and are thus indexed (important for reputation management, for example);

2. Unlike pages, groups allow to send out "bulk invite" (you can easily invite all your friends to join the group while with pages you will be forced to drop some invites manually). Groups are thus better for viral marketing, meaning that any group member can also send bulk invites to the friends of his.

Now let's go into some details:

Pages are generally better for long-term relationships with your fans, readers or customers;

Groups are generally better for hosting a (quick) active discussion and attracting quick attention.

Source by http://www.searchenginejournal.com/