Tech Lead means different things at different companies. You say you have direct reports, do you mean you do their performance evaluations or not? If so then I'd call that a manager. To me that's where the difference is. If you handle any of the "HR" parts of the process (for lack of a better term) then that's a manager.

I ask what you mean because the advice differs.

For example, I was a tech lead but not a manager. It was sort of funny, sometimes my team would ask me if it was okay if they took off or left early and I'd explain to them that "I'm not your boss" lol. Basically I'd tell them I have no problems with it but I'm not really the person who can grant that or whatever. The sort of role a tech lead has (at least in the context I was in) was maybe something like a team captain. If folks didn't have specific tasks in the sprint they wanted to work on I'd assign it to them. Most folks never really had a preference but I never wanted to seem like I was being bossy.