In my experience it’s like that (I’m talking about engineers vs eng. managers). Another significant difference is the amount of work, I believe: as an engineer I work 4h/day but those 4h are “hard” hours (fully focused) and my brain ends up a bit exhausted after. But that’s all I do in the day for work. On the other hand, eng. managers do more lightweight work, but work longer hours.
I have to say that in my experience, what my eng. managers were doing all day was: 1:1s, meetings with other managers to decide how to shift around people, interviews, being present at some sprint plannings without saying much, being present at some daily meetings without saying much.