Hi,
The HTTP application routing add-on(preview) was the previous NGINX ingress-controller addon available for AKS. Once enabled, it created an nginx-ingress-controller with only 1 instance of it.
The application routing add-on is the newly available nginx-ingress-controller addon provided by Microsoft for AKS, and it deploys a nginx-ingress-controller as well.
There's no major differences here, but the http application routing addon got deprecated and therefore to continue having the support, it's recommended to migrate to the application routing:
https://learn.microsoft.com/en-us/azure/aks/app-routing-migration