Rights Managed, or RM, refers to a copyright license which, if purchased by a user, allows the one-time use of the photo as specified by the license. If the user wants to use the photo for other uses an additional license needs to be purchased. RM licences can be given on a non-exclusive or exclusive basis. The price will depend on the type of usage be it editorial, educational or commercial.
Royalty-free, or RF, Royalty Free stock photos are in many cases interpreted as free photos. This is not true. Royalty Free refers to the right to use copyright material or intellectual property without the need to pay royalties or license fees for each use, the purchaser can use the photo multiple times on multiple projects with few restrictions. The downside to Royalty Free images is that they cannot be purchased on an exclusive basis so other stock photography purchasers may end up using the image you purchased for their campaign as well. Royalty Free is a non exclusive copyright license.
Free Stock Photography - there are many, many sites that offer very good free photographs BUT beware, everyone and their brother might be using the same photograph to depict completely different messages. If you are a corporate client you might want to stick to the Rights Managed or at least the Royalty Free Photos.