As there are many responses that present the perspective on the role of a lead vs. a manager, I am editing my answer to, hopefully, better answer your question
Pros and cons of direct reporting:
Direct report to manager is beneficial when
.. a manager is considerably involved in the project, is aware of requirements, due dates and can be a part of team meetings, let's say 3 days a week, can meet with individual members at least once in two weeks to guide them and get feedback. In short, if a manager can lead the team, it eliminates the requirement of an additional individual from budget perspective. From team member's perspective, their manager is directly aware of their performances and is in a better situation to review them.
Direct report to a lead is beneficial when
1. the manager is managing multiple projects and lot of people. This is when manager needs a lead to lead an individual project
2. Also, if a manager is not technically so sound, he/she will need a person who can take the responsibility of the project's technical wing, and lead the team.
A lead is someone who is technically sound, and has the ability to understand the product from technical and business perspective and is able to 'lead' the team by setting up goals and guiding the team members in their tasks.
A manager is one who manages the team which may include all of the above plus the HR related stuff i.e. reviews, promotions, granting days off, etc. A manager may not necessarily have in depth knowledge of each project if he/she is managing multiple projects. There may be one manager managing a QA, product and a development team, but leads are specific to one team.
I do not see the necessity to have a manager for each group (QA, dev, product, etc.) unless it is a large group.
Also, you can say that manager count will depend more on the number of people in the unit (let's say technology), and the lead count will depend more the number of teams.
Another major difference is that a manager can lead a team, but a lead does not have the power to perform the HR-related tasks.
P.S.: My answer is mainly based on my experience in the technology teams.