I'm certainly blurring the lines a bit, but I would argue that in most cases there isn't a need for both. The tech lead can be the "manager".
"Managing people" isn't a full time job in most cases. It all depends on how the organization is structured and how many non-technical tasks are being assigned to the "manager". Sometimes a manager is responsible for product, marketing, or HR tasks and all that will be dependent on the company in question.