In a distributed system there is an absence of a global state. The state is divided into many smaller units shared by a small number of computers. This distinguishes distributed computing from databases in which a consistent global state is maintained, or at least, in theory a consistent global state could be reached with the aid of a checkpoint and a transaction log.
In a non-distributed system, global state is typically well defined and maintained. Finite state machines are the heart of many non-distributed systems. Finite state machine definitely have a consistent, well-defined state.
State still plays a role in distributed systems. A small partition in the distributed system unite to define a local state. This state is maintained by this partition for a short period of time and disappears when the partition dissolves. Individual components join new partitions, share a very limited state, then dissolve into other partitions.