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A business requirement is something that is multi-customer, and a business rule represents a single customer’s approach to meeting that requirement. Product managers and analysts care about both, but product managers emphasize requirements, and analysts focus more on rules.
I can almost write a book about it, but in2 sentences I would say:
Business requirements are (out of a business analysis perspective) the processes that are essential in the day-to-day business operation. In a workflow, this defines more or less the begin and the end of the flow.
Business rules describe the way of working in the business. The basic business processes are ususally finetuned / tailored by the business rules. In a workflow, this defines the steps and different directions between the begin and the end of the flow.