der Trainer
coach
A person who guides, trains, and looks after a sports team or individual athletes.
Der Trainer hat für das morgige Spiel eine neue Taktik entwickelt.
The coach has developed a new tactic for tomorrow's game.

trainer / coach
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coach
A person who guides, trains, and looks after a sports team or individual athletes.
Der Trainer hat für das morgige Spiel eine neue Taktik entwickelt.
The coach has developed a new tactic for tomorrow's game.

'Der Trainer' (the trainer/coach) belongs to the word family of 'trainieren' (to train) and 'das Training' (training). The trainer is the person who leads the training.
Morgen haben wir wieder Training bei unserem neuen Trainer.
Tomorrow we have training again with our new coach.
The context makes clear what kind of trainer is meant. Words like 'Mannschaft' (team), 'Verein' (club), or 'Sportart' (sport) point to a sports coach. Terms like 'Seminar' (seminar), 'Firma' (company), or 'Fähigkeiten' (skills) point to a trainer or coach in a professional setting.
Der Trainer der Fußballmannschaft war mit dem Ergebnis nicht zufrieden.
The coach of the soccer team was not satisfied with the result.
In a sports context, a coach is often combined with verbs such as 'einstellen' (to hire), 'entlassen' (to fire), 'verpflichten' (to sign/hire), or 'wechseln' (to change).
Der Verein hat nach der Niederlagenserie den Trainer entlassen.
After the series of defeats, the club fired the coach.
In a professional context, a trainer is often used with verbs such as 'buchen' (to book), 'engagieren' (to hire), or 'beauftragen' (to commission).
Für das nächste Quartal haben wir einen externen Trainer gebucht.
We have booked an external trainer for the next quarter.
teacher
'der Lehrer' and 'der Trainer' are both people who teach others something or guide them. The most important difference is the area. A 'Lehrer' typically works at a school and teaches subjects like German, math, or history. A 'Trainer' coaches athletes or a team, but can also train professional skills in courses or workshops. Learners may confuse the words because both explain things and have people practice. At school, people usually say 'Lehrer'; in sports and practical training, 'Trainer' is more common.

Wegen des Turniers plant der Trainer heute ein längeres Training.
Because of the tournament, the coach is planning a longer training session today.
In der Schule erklärt der Lehrer den Kindern die neue Aufgabe.
At school, the teacher explains the new task to the children.