Hello there!
In short, two OSPF routers are neighbors if they are connected to the same subnet and share a series of common configuration information:
Same Area ID;
Same Area type;
Same subnet mask;
Same timers;
Same authentication.
They see their own OSPF RID in each other's Hello packet.
In essence, an OSPF neighborhood is a relation of two routers that allows them to see and understand each other but nothing more. In particular, two OSPF neighbors do not exchange any routing information - the only packets they exchange is Hello packets.
OSPF adjacency is formed betwen selected neighbors and allows them to exchange routing information. So, two routers must first be neighbors, only then they can become adjacent. Two routers become adjacent if:
at least one of them is DR or BDR (on multiaccess type networks), or
they are interconnected by a point-to-point or point-to-multipoint network type.
So, to sum it up, OSPF neighbors are simply routers that sit on the same segment and hear each other, but they do not engage in any closer cooperation. OSPF adjacent routers exchange routing information.