Yeah. Mastodon does not have DMs like on Twitter. They have private posts. You create a regular post but restrict it to some individuals. They have made it confusing by having a section named Direct Messages which filters out your feed to show such messages.
These messages appear in your feed. They appear in search result for you. They have @ label along with the timestamp to show that they are private. It takes a while to get used to if you are coming from Twitter.
Do remember, since these private posts are open to all users who are mentioned by their handle... If you accidentally link another user in your chats with their masto id, they would get access to that post.