At first glance it seems these two should be practically the same, right?
In a nut shell:
Local news cover broad, mainstream events that occur within a region, state, nation, and the world.
Community Journalism takes a more narrow, specific approach. It focuses on a specific geographic locale (a town or a suburb), or a community of interest or practice, or even a community of fans. Community Journalism is manged by the community (most are not-for-profit) and not by a commercial entity. Its main goal is to bring a particular community together by providing relevant content for that community.
Want to learn more?
Community Journalism (Wikipedia)
Introduction to Community Journalism Special Issue (Rural Research & Policy)