Both features are pretty similar but their use cases are different. One allows you to order your All conversations list based on active chats whereas the other helps to clean it up from old conversations that are no longer useful.
Archive conversation is a feature that removes the conversation from your active conversation list and move it to the end of your conversation list with a tag “Archived” to it. You will be able to reactivate that chat at any given time if you wish to, it just won’t clutter up your active conversation list.
Delete conversation is a feature that deletes a conversation from your list without your members being notified about that. The conversation will discontinue and be out of your head and Fleep until a chat member starts talking again in that neglected chat. At that time, the conversation reappears to your conversations list and you’re added to the conversation again. Duly noted, you won’t be seeing any of the old chat history but will still be able to see the files and pins that were included in the chat.