Send message sends a DM over lemmy. It is possible for instance admins to see these.
If you have a matrix account listed on your profile, send secure message will DM you over Matrix instead.
It's a completely different service/protocol. Activitypub (the protocol lemmy and similar fedi software uses to federate) is not well suited for encrypted communications. The main motivation is maintaining privacy.
Matrix isn't integrated into lemmy: if you want to have an account for that, you'll have to make one on a matrix server. Matrix.org is the mainstream one. I see you're a hexbear user, so genzedong.xyz may also interest you.
The only "integration" at the moment is a UI shortcut for messaging an associated matrix account.
This is more of a support question, related to using Lemmy. Please see the sidebar for a list of communities that offer support. Removing under rule #3.