While Developing for AMS websites, is there a special AEM local environment that we build with? Because with AEM 6.5, we will run the aem65-author-p4502.jar file, but how about AMS?
If you are referring to AMS as an Adobe Experience Manager Managed Services, they will provide you Stage environment which will be exact replica of production for detail testing.
So in your local and internal development environment, you can use provided AEM jar for development and testing and make sure that those are up to date with Prod & Stage AEM version.
So answer to question => it's a normal standalone AEM instance you can use for the local environment.