There's been a lot of confusion over which characters mentioned in the title above are which (especially with the release of I Am Slappy's Evil Twin).
To help end the confusion, I'm going to summarize all that we know so far.
Warning: this post contains some mild spoilers from Night of the Living Dummy, Slappy's Nightmare, and I Am Slappy's Evil Twin.
- Wally isn't Mr. Wood. When asked about them, Stine addressed them separately.
- Mr. Wood was brought to life by a magician named Kantuu using black magic.
- Both Wally and Snappy play nearly identical roles, so it is possible that they are the same character. (Or Wally was retconned out of existence.)
- Slappy and Snappy were created by Mahar using black magic that he learned from Kantuu.