What is the difference between Azure Container Instances and Web App for Containers?

Well, azure container instances bill you only for the time container is active, while webapp bill you for the time webapp exists (so all the time). that is one of the biggest differences between those.

But overall, I'd say Azure Web App for Containers is just a shortcut to run containers on existing "stuff". I've recently learned that Azure Web App for Containers offer kubernetes capabilities, so these 2 services evolve in a slightly different directions. Azure Web App for Containers is targeted at long running stuff (always running) while ACI are aimed at scheduled\burstable\short lived workloads (similar to Azure Functions).

Another difference, in addition to the other answer, is that Web App for Containers offers "slots" with which you can run multiple images on the same allocated resources to help increase utilization. As container instances bill per time used, they do not have "slots".