Mortality rates?

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Hello, could any med/bio anons please elucidate on what exactly a "mortality rate" is supposed to measure? With all of the talk about the Coronavirus going around, I have an interest in knowing what is the likelihood that someone who catches this disease is going to die from it. Intuitively, I would think the best way to measure this is to consider the population of those who have reached one of the two possible conclusions of the disease: to recover or die. With Coronavirus, these figures are 213 dead and 171 recovered, so the probability of dying should be 0.5547.

I would think that this number would be represented by the term "mortality rate", but as it turns out, this term instead is used to describe the number of dead divided by the total infected. Such a figure tells me nothing about the fate of those currently infected, so I can only wonder what it is used for. Is it describing the mortality of the disease itself? If so, what term should be used to describe the probability of a human dying from it?