To run a business is to be the one who keeps a commercial concern going — the rota, the accounts, the supplier who has not delivered.
Run is the management verb across the language: you run a shop, a department, a country, a bath. It is not the same as owning one, and the phrase describes the daily work rather than the title. Run it into the ground is the failure version, and a well-run place is the compliment. Do a business means something else entirely and nothing you would say at work.
1phraserun a businessTo manage a commercial concern.
“It is harder to run a business than to start one.”
run a business is an act of management.
Practised in Common Word Pairs