Direct chat and channel in Mattermost are almost identical, but with one big difference. Once you have created a direct chat, you cannot add more people. When you add several people to a direct chat, a new chat is created and the history is not included.
You should therefore, as a general rule, create a private channel with those you chat with, so that you can add or remove one or more people, should you need to. People you add to a channel will have access to all chat history and the channel's board(s) and playbook(s).
You can convert a live chat to a private channel should the need to add more participants arise. New participants then get access to all history. To convert to a channel, click on the person you have a direct chat with, and select Convert to Private Channel from the menu.