What's the difference between JFBCLike module and the JFBCfan module

No, that's not how both of those modules work. The JFBCFan module is meant specifically for Facebook Pages. When the Like is clicked there, it will count for the Facebook Page count. The JFBCFan module also allows you to show the Page stream and pictures of other users who have Like'd the Page.

The JFBCLike module can be used to let the user Like any URL. That URL can be a page on your site or the Facebook Page itself. If a user Like's a URL from your website, that page's Like count will increase. There is no way to combine or show the total number of Like's from all pages on your site though. Like's, in general, are for one URL (whether that's your FB Page or a URL on your site).

For either module, they will always be visible whether the user has clicked the button or not. Facebook wants them to remain visible as that allows the user to un-Like a page easily as well, which helps ensure that the user really meant the click and wasn't tricked or coerced into it some way.

I hope that helps explain, but if you have any other questions, let me know.

Thanks,
Alex

How do I get a like from the like module to count towards my FB page?

The only Like's that count toward your Facebook Page are the ones that you've linked to your Facebook Page, using either the Facebook Like (JFBCLike) or Facebook LikeBox (JFBCFan) module. Like buttons that are for individual URLs on your site only count for that specific page. There's no way to aggregate and combine Like clicks across multiple URLs.

For getting more Like's, try different things. Put the JFBCFan module in the footer area of your site or spread across both columns in the right (instead of wedged into the one). There's a lot of unused space in those columns at the bottom, so using more of it to promote the Fan page can only help.

Another ideas are to enable the stream in the JFBCFan module so user's see why they should be Like'ing the Page (they want to get your stream updates).

I hope that helps,
Alex