As stated by another reply, part of it definitely is the shift from managing people to managing managers.
The other main shift is that the scope of what you are doing goes beyond what one person can keep in their head. You can't know everything going on any more and you can't be telling people exactly what to do.
The closest analogy I can come up with it that it's kind of the like difference between "procedural programming" which you can get away with for the $1M company as compared "object-oriented programming" for the $10M+ company.
You can't possibly know every detail of every object's design and at the same time you need to have techniques to discover how well all the objects in the company are being constructed and acting as the "system engineer" making sure all the "objects" (ie: teams) still interface together well.