1. Project manage your team's deliverables.
2. Interface with other teams/EMs to unblock your team's progress.
3. Interface with product manager/owner to plan for the upcoming quarter/half.
4. Represent/sell/market your team in appropriate forums so that you keep getting high impacting projects/work.
5. Keep an eye on inter-person dynamics within the team. Address them early.
6. Hiring. For your and other teams.
7. Plan for your team member's career growth within the org. Promoting someone takes active participation of the manager with a plan in place.
8. Keep abreast of the tech-architecture that team owns. You don't want to accumulate too much of tech debt.
Typically, a "team leader" works mostly within the team; infrequently interfacing with other tams; I'd say it's 80-20 split between within team outside team focus.
EM on there other hand spend about 60-70% of their time interfacing and interacting with people outside of their team.
Of course, exceptions exist but this is how it's been in my experience.
EM is a technical role in the sense it includes managing technical projects. However, it is not an engineering role. I hold Engineering Managers accountable for the following three things:
1. People Management. You are the line manager. You must deal with hiring and firing. You should know the intrinsic motivations of everyone on your team and be able to feed those motivations. There are rote parts of the job as well, such as signing expense reports, vacation requests, and performance reviews.
2. Project Management. You are responsible for your team's delivery. If the team is blocked by something external, you need to resolve that.
3. Program Management. You should "own" your area. You should understand why the company is investing in your area and you have an opinion and a view for how your area can best accomplish the company's goals. You should understand your users/customers as well as or better than anyone.
Even if you can code, as an Engineering Manager you should not take work items for your team. If you need to switch your focus to interviewing a candidate, or a valuable team member is getting poached, or you need to talk to a customer, etc... your team needs you to take care of these things. If you have to make a choice between doing your EM job and keeping your team unblocked by delivering code, you messed up.
That's a very brief overview of how I treat the role. I know many folks disagree, so YMMV.
An engineering manager is not an engineer at all (although they may have been in the past): they only do management (of a team of engineers). The idea being that they remove that burden from the rest of the team. A team with an engineering manager would usually have a separate tech lead who lead on technical decisions.
I thought the "ing" made the role specifically one for engineers.
The idea being that engineers could continue to work doing engineering whilst moving into management. An engineering manager would be a senior engineer who also manages people: particularly those people's engineering activity.
But, I don't have much experience of this, so I might be wrong.
Engineering is being used here as a categorical rather than descriptive adjective. This person is a manager; the category of people they’re managing is engineering.
If they were happy and you described them as a smiling engineering manager, smiling is descriptive (and used as you were surmising) and engineering is categorical.
An engineering manager manages engineers. They understand the technical work about as well as the people they manage, so that they can give relevant coaching. They also understand management principles that make engineering projects successful (WIP counts, release process pros and cons, etc). In other words they know how to structure work flows.
There's a big difference there, managing a few people is what I know as a Team Lead while managing a group means managing a few teams with their team leads.