I'd like to develop a game, and try it out mainly on the Playstation 4.
Can I build any game, or app, and release it on the Playstation Store? Or does Sony only allow what it wants in the store, much like Apple and the AppStore? Note that I'm not asking how to build a game, but whether or not there are restrictions that would prevent me from releasing certain kinds of games or applications to the Store.
No, you can't release "anything" on the Store. So yes, to some extent the store, like all software portals like it (including Apple's App Store, Steam, Xbox Live) could be considered a "walled garden."
The question is how walled, really. Unfortunately details on the licensing agreements you sign when you become a licensed PlayStation developer aren't public (at least, not that I could find), so it's difficult to provide solid examples sans legal entanglements.
That said, the Store requires a license agreement to publish to, and it would be baffling and foolish for Sony not to include a clause in that agreement that would allow them to block the publishing or distribution of your product if they deemed it inappropriate for their store. After all, they have their brand image to worry about and consumers won't really care if you are selling a horribly inappropriate or scammy game on the store, they'll focus on the fact that Sony let you.
Anecdotally, by browsing the store you can see very few things labelled "apps" (as opposed to "games"), so it's unlikely that Sony will want you to try to sell, for example, a spreadsheet program.
