The coronavirus death totals are from confirmed deaths where there is an attending physician signed death certificate. The seasonal flu numbers are CDC estimates.
As with all illness, someone has to diagnose it in order to treat it. So you are correct that “coronavirus cases” mean someone has diagnosed the illness, usually via testing. But COVID-19 is such that some people have died so suddenly that there wasn’t time for a test: Severe symptoms, on a respirator in ICU, and death.
“A New York Doctor Who Died After Fever and Cough Was Never Tested for Coronavirus, Highlighting the Limits of the Official Toll”
https://time.com/5818062/new-york-doctor-coronavirus-death-toll/
Meaning the fatality rate for Covid does not come close to representing reality since those tested make up a small minority of the infected, and are the most likely to have severe cases, while your 0.013% fatality rate for the flu is also way off, since it is based upon the wrong numbers.
Universal or random extensive testing for Covid - the more the better - is needed to determine its lethality, and surmising a death rate from estimates based upon such testing is to be preferred versus simply the relative few that are tested because they have symptoms.
We have the CDC morality rates for the flu per state for 2018 (13 states above 17 per 100,000 total population) and for Covid here (only one state above 17 per 100,000 people, as of April 9), and according to estimates, between 61,000 to 80,000 Americans died during the 2017-2018 season, the latter being the highest death toll in 40 years. During that 2017-2018 season, the percentage of deaths attributed to pneumonia and influenza (P&I) was at or above the epidemic threshold for 16 consecutive weeks. Nationally, mortality attributed to P&I exceeded 10.0% for four consecutive weeks, peaking at 10.8% during the week ending January 20, 2018, (https://www.cdc.gov/flu/about/season/flu-season-2017-2018.htm) with older Americans dying at a rate of 169 Americans a day, or seven people per hour. (https://www.aarp.org/health/conditions-treatments/info-2018/older-flu-deaths-rising.html
It is estimated that about 80% of those infected with Covid-19 experience a mild case [WHO said the like] – about as serious as a regular cold – and recover without needing any special treatment. Meanwhile a study in Iceland reports that as of April 11, the country has “tested 10% of its population for coronavirus - a figure far higher than anywhere else in the world -” [and with fatality rate of about 0.4%] and that “about half of its citizenry at any given time who have coronavirus but don't know it, will be asymptomatic” (show no symptoms), which is “a large percentage many experts studying the virus have suspected, but have had little firm data to corroborate.”
Another report is that those who are most vulnerable to death from Covid-19 are the aged with certain other heath conditions, thus 80 percent of US coronavirus deaths are people 65 and older. Then again, America murders over 2,000 of the most vulnerable souls a day (2017: https://www.guttmacher.org/fact-sheet/induced-abortion-united-states).
Despite such headlines - which does not say he was never tested after death - it stands to reason that most deaths by Covid are tested as being such, either because being that sick mot people seek medical help, or are tested after death. Moreover, deaths that are missed can be made up for by adding deaths by Covid based upon presumed cases, such as NY did, adding 3700 presumed cases in one day, all presumed based on their symptoms and medical history. In NYC any patient who has had a positive coronavirus test and then later dies - whether at home or in a hospital - is being counted as a coronavirus death. (https://www.nytimes.com/2020/04/10/nyregion/new-york-coronavirus-death-count.html) On average year round, about 158 people died every day in NYC from various causes in 2015. (https://www.health.ny.gov/statistics/vital_statistics/2015/table31a.htm)