What is the name of the relationship between two ospf devices that are connected together and exchange link-state information?

FULL neighbor state.

(FULL/DR or FULL/BDR)

Explanation:

The fact that the routers are neighbors is not enough to guarantee an exchange of link status updates; they must form adjacencies to exchange link status updates. Adjacency is the next step after the process of establishing neighbors. Adjacent routers are routers that go beyond a simple Greeting exchange and act in the database exchange process. To reduce the amount of information exchange in a given segment, OSPF selects a router as a designated router (DR) and a router as a designated backup router (BDR) in each multiple access segment. The BDR is chosen as the backup mechanism in case the DR fails. The idea behind this is that routers have a central point of contact for the exchange of information. In order to verify if two routers have established an adjacency, you can use the command: show ip ospf neighbor.

Here is an example:

R1#show ip ospf neighbor

Neighbor ID   Pri         State               Dead Time     Address      Interface

203.250.12.1    1     2WAY/DROTHER  0:00:37   203.250.14.3  Ethernet0

203.250.15.1    1     FULL/DR                0:00:36   203.250.14.2  Ethernet0

203.250.13.41  1     FULL/BDR              0:00:34   203.250.14.1  Ethernet0

because you most likely sighned up