der Sport
sport
Physical activities done for fitness, fun, or competition.
Ich mache dreimal pro Woche Sport, um fit zu bleiben.
I do sports three times a week to stay fit.

sport
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sport
Physical activities done for fitness, fun, or competition.
Ich mache dreimal pro Woche Sport, um fit zu bleiben.
I do sports three times a week to stay fit.

To express that you do sports, you use the verbs 'machen' (to do) or 'treiben' (to practice/do). 'Sport machen' is the most common variant in everyday language.
Ich versuche, regelmäßig Sport zu machen.
I try to do sports regularly.
When talking about the activity 'Sport' (sport) in general, the noun is usually used without an article. You say 'Ich mache Sport' (I do sports), not 'Ich mache den Sport'.
Sport ist gesund und hält fit.
Sport is healthy and keeps you fit.
The word 'Sport' (sport) is the first part of many useful compound nouns. Examples are 'die Sportart' (type of sport), 'der Sportplatz' (sports field), 'die Sportkleidung' (sportswear), or 'der Sportverein' (sports club).
Fußball ist eine sehr beliebte Sportart in Deutschland.
Soccer is a very popular sport in Germany.
When 'Sport' (PE/sports) is used in connection with 'Schule' (school), 'Stundenplan' (timetable/schedule), or 'Note' (grade), it always refers to the school subject.
Meine Lieblingsfächer in der Schule waren Kunst und Sport.
My favorite subjects at school were art and PE.
movement
'der Sport' and 'die Bewegung' can both have to do with physical activity. 'Sport' usually means a specific activity, often with rules, training, fun, or competition, for example football, swimming, or running. 'Bewegung' is broader and more general: even going for a walk or climbing stairs can be 'Bewegung', especially when talking about health. The words can be confused because sport is also movement. But not every kind of movement is sport. If you are talking about a sport or competition, 'Sport' is more natural. If you are talking generally about being active for your health, 'Bewegung' fits better.

Nach der Arbeit macht Ali gern Sport im Fitnessstudio.
After work, Ali likes doing sports at the gym.
Die Ärztin sagt, dass mehr Bewegung gut für den Rücken ist.
The doctor says that more exercise is good for the back.