What is the difference between alternate-flow and sub-flow in the use-case diagram?
In effect these are different names for the same thing, or near enough not to matter. Strictly speaking, an alternate flow is something the user or customer would recognise as an alternate scenario, while a sub-flow is not necessarily so (though usually the user or customer would recognise it if pointed out to him or her). But don’t worry about the naming conventions – use whatever flows you need and let the ivory tower folk worry about what to call them. And try not to use more flows than you need… but sometimes we subdivide to make our work of describing the system easier, which is why terms such as “sub-flow” get coined. I’m not sure whether “Use Case Diagram” is pertinent – flows usually get shown on activity diagrams or sequence diagrams – but let’s not be picky. I hope I’ve answered your question.