A boy is running in a small room and some native speakers command "No running", not "don't run".
When do we say "no running, no talking" and when saying "don't run", "don't talk"?
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Notices asking the general public not to do something in that place, such as NO SMOKING, are worded in that way. If used as a command to an individual person, the sense is "Don't do that because it's not allowed here". It could be dangerous for a child to run about among other people in a small space, so I suppose the people meant to tell the boy "This room isn't the right place to be running", rather than asking him personally to stop.
"No running" is a rhetorical choice, to influence without a direct order.
"Don't run" is a command using the imperative. It is directed at a person. It implies "You! Don't run!"
"No running" is a noun phrase. It is less direct, it may be understood as "There is no running here", so it doesn't imply "you" particularly.
A person might use "Don't run" to be direct, or because the rule only applies to that one person. Or "No running" to give the same instruction while avoiding conflict. Because "No running" isn't directed at "you" it implies "This rule applies to me, you and everyone else". This is a rhetorical choice to get someone to do something by making them realise that it is a general rule and not just an order from me to you.