Clearing a chat (from the conversation's 3-dot menu) removes the message history from your own view up to that point in time — it doesn't delete anything for the other person, and it doesn't stop new messages from continuing to appear afterward.
Hiding a conversation removes it from your chat list entirely, as if it isn't there. If the other person sends you a new message after that, the conversation automatically reappears in your list — hiding it isn't permanent and doesn't block the other person from reaching you (for that, see blocking a player in the Account & Profile section).