Tech leads work through their team to deliver. To work through their team, they need to drive to consensus. To do that, they need the support and understanding of their team, so they need to lead. To lead, you need to manage. That doesn't make a TL responsible for firing or resolving interpersonal disputes, but it certainly makes them responsible for coaching/mentorship/up-leveling in a much more direct and often valuable way than a manager.
Tech leads work through their team to deliver. To work through their team, they need to drive to consensus. To do that, they need the support and understanding of their team, so they need to lead. To lead, you need to manage. That doesn't make a TL responsible for firing or resolving interpersonal disputes, but it certainly makes them responsible for coaching/mentorship/up-leveling in a much more direct and often valuable way than a manager.