What is the name of a notification that looks like an HR chat?

The most accurate terms are chat-like notification, recruiter-like prompt, or chat-led reactivation. If the message starts an early interaction to make users open a job post, conversation seeding is also a relevant term.

Does an HR chat in a job app always mean it is a bot?

No, not always. The chat can come from a human recruiter, an automated template, a recommendation system, a chatbot, or a mix of several mechanisms. From a UX perspective, the key point is how the message is designed to feel like a personal conversation.

What is the difference between conversational apply and chat-like notification?

Conversational apply is a job application process designed like a conversation, usually after the user starts applying or shows interest. Chat-like notification is a notification or inbox message designed to look like a chat in order to make users open the app or view a job opening.