is AWS Management Console and AWS Console Home the same thing?

Yes, you are correct, they are the same.

AWS Management Console is a web application that allows you to control and manage your AWS Account and to use the AWS services and resources by providing you access to various service consoles. When you first sign in, you see the console home page.

So essentially, the console home page is just one of the pages you can open in the AWS Management Console. The console home page gives you an overview of your AWS Account.