In my previous jobs I've done a lot of project management (PM), especially with clients' teams. I.e. I organised team work, established milestones, controlled their completion, etc. These were teams of considerable size.
In my last job interview I was told I couldn't be considered for a senior consultant position because I have never acted as a PM for teams of several consultants. They told me at their company this would be teams of 1-2 people (apart from me obviously). They would expect me only to coordinate the work of my team, no external people.
Could you help me to understand whether these are really two different competencies? For me, PM is one set of skills. Of course, we can talk about different types of PM (agile, waterfall), PM in different industries, more IT-oriented PM and less IT-oriented PM, etc. but if that's constant, is the difference between coordinating the work of your team - consultants - and clients' teams really so considerable?
Just a remark to avoid misunderstanding: I work as a consultant. I.e. If I did PM work with clients' teams this means I worked with external people. Teams of consultants would be "internal teams" for me.