Rate

A rate is a count divided by the size of whatever produced it: a population, a stretch of time, a number of trips, an amount of exposure. Two things separate it from a proportion. Its numerator counts events, which need not be a subset of what the denominator counts, so a rate has no ceiling of 1. And it keeps its units, so a rate means nothing until you say per what. Every proportion can be restated as a rate, since 0.15 is 15 per 100 and 150 per 1,000. The reverse fails: no proportion equals 60 miles per hour.

The base decides the answer because it decides the question. Suppose country X records 1,200 road deaths in a year, with 6 million residents driving 90 billion vehicle miles, and country Y records 900, with 9 million residents driving 30 billion vehicle miles. Per 100,000 residents, X is at 20.0 and Y at 10.0. Per 100 million vehicle miles, X is at 1.33 and Y at 3.00. Both pairs are correct and they point opposite ways, because one answers how risky it is to live there and the other answers how risky a mile of driving is there.

"Country Y has the lower road death rate." There is no such thing as the rate, only a rate per a stated base over a stated window: Y is lower per resident and higher per mile driven. The window matters as much as the base, since 7 per 1,000 per year and 7 per 1,000 per decade differ by a factor of ten.

Plenty of quantities called rates are arithmetically proportions. An unemployment rate divides unemployed workers by the labor force; a response rate divides replies by people contacted. In both, the numerator sits inside the denominator and the value cannot pass 1. What makes 84 emergency room visits in a town of 12,000 a genuine rate, $84 / 12000 = 0.007$ visits per person per year or 7 per 1,000 per year, is that one person can turn up twice.