Hi Liya,
You can separate those two blogs based on the path in the content tree (pages application). Widget 'Show latest blog post' is nothing else then simple repeater which getting all blog posts under specific path (blog) and order them by BlogPostDate field (usualy DESC). So if you want to show that in different way, you can clone, f.e. 'Department latest blog posts' widget and make it to be generic by checking Display field in the editing form for Path field on Properties tab. In that way, each time when you add new widget, you can select will it be for 'Department' or for 'Company' blog.
You can always clone it twice and just update path field for both to look at correct places.
Best regards,
Dragoljub