you ever wonder why people refer to the state of washington as "washington state", and not simply "washington"?

the obvious answer is because of the nations capital sharing the same presidential name, but why not call the west coast state simply as washington, and refer to the east coast district as "washington district"?

after the end of the mexican cession, the united states took possession of many states, california being included. yet, we call it simply as "california", and the mexicans refer to their part of it as "baja california".

if it belonged to them first, why dont we let them keep the name california, and call our state "north california", or "alta california" or some other name to distinguish the fact we acquired our territory later.