Is a galaxy s4 the same sim as iPhone 4?

Will the SIM cards work in each phone?

I believe both phones take a micro sim, so yes, it should fit. If both phones are from the same provider or are unlocked than you shouldn't have any problems.

YES, they are.

The Galaxy S4 and the iPhone 4 both take the Micro Sim, but the new iPhone takes the mini sim which is just the chip and no other plasticky bits.