They’re the same as in nobody is forced to get the vaccine. Nobody will be threatened with state violence for not getting the shot. They’re just barred from a lot of facilities for the choice they made. We do similarly for children whose parents refuse to give them measles shots.
Enforcement, naturally, varies. In Manhattan, I’m constantly asked for card and ID. In Long Island, it never happened.
Due to Denmark's high vaccination rate and widespread following of anti-COVID measures their delta surge in cases was in the bottom half for Europe (and peaked about 60% below the US delta surge), and their delta death surge was almost undetectable when graphed on the same scale as the rest of Europe (their peak was around 8% of the US peak).
Denmark seems to have made it to the stage where COVID is now just another circulating cold virus (joining the previous four coronaviruses that have become endemic in humans and are responsible for about 20% of colds). About a month ago they ended all COVID restrictions. That's why no one has cared about your vaccination status recently.
The U.S. won’t jail you if you refuse the vaccine. But you have to stay home. This is functionally identical to the Scandinavian solution, minus public buildings and minus a federal vaccine certificate.