Does the Samsung Galaxy S4 have all apps available on the iPhone 5?

Also, do the apps play just as smooth as they do on the iPhone?

Nope to both questions.

There are some IOS exclusive games and apps that you won't find on the App Market, but the majority of the apps and games are the same. Also, the games will run just as smooth, if not more smooth than the iPhone since the GS4 has 2 Gigs of ram while the iPhone (5) has 1 Gig.