The town itself is not the same. Silent hill from the Game universe is a quiet little resort town on Toluca Lake. The one in the movie was a mining town in the mountains of West Virginia.
It's still technically the same town though. It's still Silent Hill, and it still has the strange mystical powers it did in the game, although they were possibly brought around in a completely different way (if they were brought about before the events of the first movie we'll never know. No one's really left in town to swap ghost stories around a camp fire. D: )
Silent Hill in the games is supposedly in Maine, not West Virginia, and has a totally different theology surrounding it that more represents the Puritans with the Salem witch trials than a devil worshiping cult trying to raise a demon.
We still don't know where the one in the games is, do we? Wasn't there a topic floating around about how the cars in each game had a prevalent license plate from a different state? I'm not arguing, in case you're wondering, I've just always thought that the location was meant to be ambiguous. Although if it is in Maine, that's quite fine. They have good lobster. XD
"Believers hearken to me! Twenty score men and seven thousand beasts."
The believers, and the twenty score men are the cult, and the seven thousand beasts are the monsters.
So silent hill 2 does have gods.
I'm aware of the Book of the Crimson Ceremony, but that ending, to my knowledge, isn't considered canonical since it can't be achieved on the first run through. That means, in the context of the gods being in Silent Hill 2, it can really be seen as void. It's more of a nod to the history of the town, and a little add-on for the Restless Dreams/Directors Cut of the game.
James actually preforms the ceremony in the Rebirth ending, and Walter's ceremony uses all the same items that James' does.
While Walter's Silent Hill is a reality thanks to the cults influence on Walter, and their beliefs, it really doesn't mean anything. It doesn't strengthen anything; not really.
Dark Alessa not only states that she has many names, but also says "Right now, I'm the dark part of Alessa". Implying that it/she existed before that.
You're forgetting that Dark Alessa believes she's the Devil. That means that she thinks she existed before, but she actually didn't. She's a complete product of Alessa, there was no outside interference involved with her summoning. And also look at JRamirez35's little tidbit there. Alessa's been called a lot of things in her life having something to do with evil, it's likely that she's referring to these.
I once was lost, but am now profound.