der Teilnehmer
participant
A person who actively takes part in an event, course, competition, or activity.
Alle Teilnehmer des Marathons erhielten eine Medaille.
All participants in the marathon received a medal.

participant
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participant
A person who actively takes part in an event, course, competition, or activity.
Alle Teilnehmer des Marathons erhielten eine Medaille.
All participants in the marathon received a medal.

'Der Teilnehmer' (participant) is a person who 'teilnimmt' (takes part). The word derives directly from the separable verb 'teilnehmen' (to take part), which means 'an etwas partizipieren' (to participate in something).
Wer am Gewinnspiel teilnehmen will, muss sich als Teilnehmer registrieren.
Anyone who wants to take part in the prize draw must register as a participant.
To say what someone is participating in, German uses the preposition 'an' followed by the dative. For example: Teilnehmer an einem Kurs (participant in a course), an einer Konferenz (at a conference), an einem Spiel (in a game).
Die Teilnehmer an der Diskussion waren sehr engagiert.
The participants in the discussion were very engaged.
You can easily recognize the meaning from context. If you hear the word in an automated phone announcement, 'Teilnehmer' (subscriber) refers to someone in the telephone network. In almost all other situations (sports, education, events), it means a person who takes part in something.
Die Teilnehmer des Sprachkurses kommen aus verschiedenen Ländern.
The participants in the language course come from different countries.
player
'der Spieler' and 'der Teilnehmer' both refer to people who take part in something. 'Spieler' is used when it is really about a game or a sport, for example soccer, tennis, or a board game. 'Teilnehmer' is more general and fits courses, events, competitions, or meetings. The words can be confused because a player is also a participant in a game. But in a language course or a meeting, you would normally say 'Teilnehmer', not 'Spieler'.

Am Wochenende begrüßt Lukas die neuen Teilnehmer im Kochkurs.
On the weekend, Lukas welcomes the new participants in the cooking course.
Nach dem Foul spricht der Schiedsrichter mit dem Spieler.
After the foul, the referee speaks with the player.