How does scaling out work in Azure App Services?

Question

I am trying to wrap my head around the concept of Azure App Service plan and Azure App Services, with no luck.

My understanding is that an App Service Plan defines the c

Answer 1

My understanding is that an App Service Plan defines the capacity and the pricing, all apps assigned to a specific App Service plan will share the same resources, is that right?

Yes.

If that is right, then what is the benefit of the scaling-out? If the scale out will create more instances of the same app which at the end will be hosted on the same App Service Plan (sharing the same resources)?

No one forces you to put all your apps on the same App Service Plan. When you create an App you put it into some App Service Plan. All the Apps on that (and only that) App Service Plan would share resources, but you could create a lot of App Service Plans.
Also, when you scale out you create more PaaS instances of the VM's hosting your App, so when you scale out you are not getting another App Pool in the same IIS, you are getting another App Pool on the other IIS on the other VM.

edit: to clarify the comment, the App Service Plan is a collection of Windows VM's with IIS installed on them. All the Apps assigned to that App Service Plan are hosted on ALL the instances of those VM's, when you scale out or scale up you change the number or capacity of those VM's.
There's no temporary App Service Plan. You pay for the Service Plan, not for the App. Apps cost nothing, they are simply consuming resources on the Service Plan, its the Service Plan that "eats" money. You are getting billed according to the Service Plan tier and scale.
Pricing is based on the size and number of VM instances you run.