What rate means
"Fast" and "slow" are good enough for a comparison, but science needs something measurable. To get it we look at how much change happens as time passes.
Rate of reaction
The rate of reaction is the amount of change that takes place in unit time.
The question, in other words, is not "how soon is it over?" but "how much changes per second, per minute or per hour?" The second question can be answered with a number.
Speed
The distance travelled in unit time. Metres per minute.
Rate of reaction
The change that takes place in unit time. Grams used up per minute.
The likeness is not a coincidence. Just as motion divides distance by time, here we divide the amount of change by time. The next page is that division.