If copyright is involved, the rules are the same for Facebook and blogs. In short, don’t infringe on someone else’s material; if someone infringes on yours, register a DMCA complaint.
Here’s some background information
- Facebook’s take on copyright infringements: https://www.facebook.com/help/249141925204375/ (they say that if you think something you want to post is copyrighted, don’t post it).
- What to do if someone steals your text, from WordPress’s point of view: https://en.support.wordpress.com/copyright-infringement-what-to-do/
Keep in mind that when you share something on Facebook (unless you copy it to your computer and re-paste it), you just have a “window” into the original picture or video on your timeline, not the actual picture or video. So copyright issues don’t really come up.