I go to school __ foot. (on/by)

My book says

"On is used to indicate mode of movement"

"By is used to indicate mode of transport"

Give me the answer, explanation is needed as i don't understand what is difference in movement and transport and what will fit this line.

Dear student,
I go to school on foot.
A​​​​​ person goes to school by bus/train/car.
As bus/train/car are mode of transportation.
Regards   

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what is the reason?
 
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I need a proper explaination
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