I think the main difference between the two is, IAP aims to replace VPN requirements for Enterprises. It only integrates with Google accounts and it seems to go hand in hand with GSuite. So they are more B2B oriented. We hide our staging servers behind IAP for instance.

Amazon's solution seems to integrate with a few other identity providers and gives the developers the tools to do authorization after authentication is done. It seems to position this more like a B2B2C. Although it feels like it already subsumes Google's IAP by doing so.

This is my understanding by reading the article on Amazon, I haven't actually used it.