In many organizations the line manager is the tech lead (at least at the lower levels of the hierarchy). Having a separate leader and manager is only useful if you aim to create a barrier between technology and the business, which is typically not a very healthy thing if you're a technology-driven company. Nevertheless it's a common practice in places where technology is just a supplier servicing the business.

And a tech lead is very much about directing people. You need to have a vision, inspire them, make sure everybody is making progress towards the goal etc. It's hands on and operational, but that's where collaboration between people is most important.