Project manager vs People manager: two identical jobs?

Let’s say you’re a great project manager. Does that automatically mean you’ll be a good people manager? Or vice versa?
This question came to me following a conversation with a colleague. He did not understand why he would not make a good boss when he was so well liked in the context of all the projects he had led.
These are two different jobs, in my opinion. Being successful in one does not guarantee success in the other.
Naturally there is plenty of overlap between the two. Both roles coax a team into reaching a target based on a vision. Both require keeping a lid on costs, sticking to deadlines, managing people and knowing how to put ideas across.
The difference is seen in terms of timeframe.
A project has a set lifetime in which a clearly stated goal needs to be reached. In an organisation, the term is unlimited and the goal is expressed as a longer-term vision.
For example:

In practical terms, how do these differences affect the way a team is managed?
The project manager manages according to a shorter timeframe. The project team shows determination and can be trained further to reach the goal. Part of the process is defined by the team along the way, as every project is unique.
The manager is working according to a long-term perspective. Project after project, this person’s team must stay motivated and continue finding meaning in its work.
Perhaps an overstated analogy would be likening a project manager to a soldier and a people manager to a farmer.