Alinor and Valenwood are the same place practically...
Most certainly not!
True, they're both ruled by the Thalmor, but in terms of lore they're very, very different.
Valenwood is home to Walking Trees which house the Bosmer cities. The Bosmer live under the Green Pact - they eat their slain enemies, are purely carnivorous and do not harm Valenwood's natural resources for ANY reason. They even have to import wood for their houses!
I'd suggest looking up Valenwood on The Imperial Library or even UESP for more information.
Edit: The Thalmor renamed Summerset Isle 'Alinor'. So the nation shares a name with its Capital.