I thought about this when developing the app.  I always thought that "share" made more sense than "like".  But then I went to review the Facebook developer documentation and they said:

What happened to the old Share button?

We deprecated the Share Button when we launched the Like button, because the Like button improves clickthrough rates by allowing users to connect with one click, and by allowing them to see which of their friends have already connected. For reference, the Share button documentation is still available here.

http://developers.facebook.com/docs/reference/plugins/like/

So I just kept the Like button ....

Thanks for the feedback!