It is exactly the same, another country's leader coveting a land they have decided they want.
Putin's war is more brutal; however, Russia and Ukraine have a history of being part of each other's territories. Unwanted, obviously on much of Ukraine's part but nevertheless it's there.
USA has no history with Greenland apart from its military base, negotiated with Denmark and Greenland. Trump is a bully....a man child who sees something he wants and will create havoc until he gets it.
Europe will not be safer if Trump gets Greenland, quite the opposite. USA itself may be safer because it can expand its territory and launch missiles from an area which doesn't impact the USA mainland. It will not benefit anyone else. Furthermore, USA will then have access the rare earth minerals, metals and even more importantly, uranium, which are currently buried under the Greenland ice sheet but which are becoming more and more accessible as that ice sheet melts (global warming is much faster up there in the Arctic).
Russia is not after Greenland and doesn't need it; it already has masses of these resources, they're hidden under the ice sheets of Siberia. China would like these resources which is partly why they have teamed up with Putin, China has declared itself a "near Arctic" state - the Russia-China cooperation works well because Russia has the resources but not the manpower, China has the technology and a load of people it can supply to work that technology. China is therefore not currently after Greenland either, an incorrect statement on Trump's part.
Canada also has many resources under its northern ice sheets (Northern Territories) which is why Trump would like them as well, but Canada is a bigger proposition and not as easy to take over. The USA's own bit of the Arctic (Alaska) is limited in what it can produce and what's under there, and it isn't as vast as Greenland.
Like China, USA is playing the "long game"; they know full well that the future, where global warming really takes a hold, isn't so very far away. The resources we have (eg. oil in the middle east, current mineral supplies, even water and food security) will be threatened and will eventually run out. Meanwhile, the melting Arctic will yield up new resources, also new land which will eventually grow crops and be where people begin to live as it becomes too hot further south. Even the fish will migrate to cooler seas north, there will be very little left elsewhere. Whoever 'owns' some of the Arctic will also hold enormous power at that point.
That's before we even consider other factors like military bases, sea route access for shipping goods/militarisation, and nuclear weapons, including northern airspace.
Because many everyday citizens don't see global warming as a major factor in their lives (busy with cost of living, children, mortgage, jobs) many do not realise how serious the "scramble for the Arctic" (comes from the title of one of many research papers on this) is, nor how soon it will impact on our future - it's "too far away" in their eyes.
Greenland is a big, big problem which we need to take far more seriously.
[I have lived and worked in Scandinavia in past years before retirement, travelled up and down east and west Greenland, seen the work of the Arctic Council, taken part in global warming research projects in northern Norway, seen first hand the issues with mining, militarisation and nuclear weapons in western Russia/Svalbard and so forth. I do have extensive knowledge on the subject and would urge anyone who is interested to inform themselves and speak up to friends, neighbours, action groups, MPs as you feel necessary].