I think the meaning of 'rate' may be generalised to 'amount (of change) relative to a unit of measure'. This applies to 'speed' (change of distance/unit of time), 'interest' (% change/year,..., heart beat, and so on. This is also (almost) the same meaning as 'ratio' (which is usually a quotient of amounts of the same unit of measure).

At any rate, this 'rate' is not precise and so confusing at times. ;-)