I don't get the difference between what's considered an “operation” and a “dependency” in Azure Application Insights.
What are the criteria for which something falls under one of the two sections?
For a web application, Operations represent incoming requests ("requests" table in Logs) and Dependencies represent outgoing requests ("dependencies" table in Logs).
For non-web applications (for instance, for a worker role processing Event Hub messages), there is no such thing as incoming requests. That was one of the rationales to name this tab Operations and not Requests (which is still widely used in the rest of the product).