Once upon a time, there was IRC for single-stream chats, and NNTP for threaded ones, and all was good. Twitter used to be one of the former, but then they noticed that users were using the "@name" convention to simulate replies, and started officially supporting it. Instead of a single conversation, or a tree of nested replies, they created some unholy thing partway between the two, that serves neither role well.
Twitter threads are a tree, but the representation in Twitter's web interface and mobile apps is linear and it's not obvious which tweets are in response to which. There are hints in the interface if you're aware of them, but it's easy to get lost.