I've been wondering about this question for a while. I'm aware that Job Titles are not completely meaningful (specially, in the financial sector) but still, calling one as 'Project Manager' should represent a standard.
The Job Title usually goes along with the role the professional executes on his daily work. Controlling Scope and Schedule is the basics, and usually it implies in leading a team. However, there's one Constraint, the cost, which - I believe - would differentiate a 'Team Leader' or a 'Project Leader' from a real 'Project Manager'.
Looking for the PMI definition, it states that
(...) project management brings a unique focus shaped by the goals, resources and schedule of each project
which makes no clear reference to costs. In this same link, is mentioned the knowledge areas the PM is expected to cover, which are:
- Human resources
- Risk management
- Stakeholder management
Where some of them, as previously stated, are 'basics' for a Project Leader / Manager, and others will... well... fall into a 'gray' area that varies from company to company and maybe from market to market.
I've checked some similar questions like 'The difference between a Functional and a Project Manager' and 'The difference between a Project Manager and a Project Leader' and turns out that the former is focused on two specific and not overlapping roles (from my point of view) whereas the latter is understanding both Leader and Manager from a 'controlling' perspective (by force or by willing) which is not what I'm referring to in my question.
Bottomline: Is it correct to call one Project Manager even if this 'Leader', 'Manager', or any other expression we want to use, does not deal with project costs?