Denmark counts all corona deaths. Could it be that your Danish source thinks that there are no separate statistics for deaths in nursing homes? You should ask them to provide a link of some kind.
I assume that the vast majority of deaths (maybe all deaths) from Covid-19 are in ICUs. I can't imagine that any difference is made between where people were before they were transferred to a hospital and then to an ICU and placed on ventilators/respirators.
I very recently saw the definition of what counts as a death from the virus, and I think it was anyone who dies from whatever cause if that person has been tested positive for the virus in the last two months. And then, of course, there are the post-mortem tests. The first registered Covid-19 death in Denmark was a patient who died from a heart condition but was tested positive for the virus post mortem.
I'll try to find the official defintion of Covid-19 deaths in Denmark.
In the meantime:
Deaths per million (total) (TV2.dk, April 29, 2020)
Sweden: 235 (2,355)
USA: 177 (58,355)
Denmark: 75 (434)
Norway: 38 (206)
Finland: 36 (199)
Iceland: 30 (10)
Percentage of population tested - Percentage of positive tests
Sweden: 0.7 – 14.1
Finland: 1.1 – 6.5
Denmark: 1.7 – 7.8
Norway: 2.7 – 4.9
Denmark cases of hospitalizations and deaths peaked April 1 or April 2:
Denmark: April 1 or 2 --> April 28
Hospitalized: 535 --> 284
In ICU: 153 --> 66
On ventilators/respirators: 138 --> 50
Deaths per day: 20 --> 6