If you are just starting with Asana, you might confuse the word « Conversations » in the interface with the « comments ».
When you use the advanced search, the last tab says « Conversations ».
When you open the member notification settings of a project, there are checkboxes related to « Conversations ».
Conversations is a dedicated feature that has nothing to do with comments on tasks. Each project and team have a conversation tab at the top (sometimes in the « More » menu). Also conversations do have comments themselves
So the advanced search option is about looking specifically inside Conversations (the regular search looks into comments). And the notification settings are about getting notified about a new conversation (not the following comments, unless you opted in).
Still confused? Comment below!