"Application Engineer" probably means an engineer who does high-level technical support for customers, as it did when I worked for a company which sold products to technical users in the 1990s. Your customer buys some complex electronic part or system from your company and then tries to use it in some demanding application. When it doesn't work as expected, an "AE" is called to debug the setup and educate the customer on how to properly use the company's product. In such a role, you're not part of the product development organization, so you might spend all your time training or debugging (edit: adding for clarity - training customers and debugging their systems), and none of your time writing any code; and anyway what code you write might well be examples or proofs of concept for customers.
