Yes, in the countries that officially label cases as such, the "serious" ones are those needing hospitalization. Others are being told to remain at home and stay isolated. Also note that even some of those who remain at home get worse later, and some die before they can be hospitalized. The major point that you have to be aware of is that the hospitalizations and deaths come later and that the doubling time is short. Also, the doubling time of 3 days means that the country which has 1/2 of the coronavirus allocated bed capacity on 1st of April won't have enough beds starting with 4th.
Also, please try to analyze as much countries (I know about European ones) as possible. Go for the official sources, or the pages in the Wikipedia on local languages, you'll find much more reliable data, and for some countries even official "in hospital" "in intensive care" and "deaths" numbers.
at that moment: "the total number of UK deaths 759, with 14,543 confirmed cases."
Now: "47,806 confirmed, 4,934 dead."
That they understand that it's going to grow more: "The National Health Service freed up 30,000 beds by discharging patients who were well enough and delaying non-emergency treatment,[342] and acquired use of 20,000 beds in private sector facilities." (wikipedia)
But they still also hope that the current measures will slow down the growth.
They test less than some countries though, but you can see the factor of hospitalizations against the deaths, and note that deaths reflect many days older (and smaller) "cases" count and hospitalizations are somewhere in between.
The time lag is a valid way of deriving this number. In places that do a lot of testing, the number does look lower than 20%. Especially considering most only test those that go to the hospital.
Also, please try to analyze as much countries (I know about European ones) as possible. Go for the official sources, or the pages in the Wikipedia on local languages, you'll find much more reliable data, and for some countries even official "in hospital" "in intensive care" and "deaths" numbers.