Which is the Danish Versailles?

Yes they are indeed two different palaces very close to each other.
Frederiksborg (meaining Frederik's castle, named after King Frederik the 2rd) is the largest renaissance palace in Scandinavia. It is very impressive and also hosts the museum af national history and also has a large barouqe garden. Most of it is open to the public.
https://en.wikipedia.org/wiki/Frederiksborg_Castle

Fredensborg Palace is a barouqe palace and one of the main recidences of the Danish Royal Family and is often used for royal weddings and state visits. The building itself is not that impressive and much is closed to the public, but it has a large park and garden complex. https://en.wikipedia.org/wiki/Fredensborg_Palace

Frederiksborg is the most impressive, but the comparison to Versailles is a misnomer, since Frederiksborg is older than Versailles and build in the style of Dutch Renaissance, whereas Versailles is French Barouqe.
Fredensborg on the other hand is build in the style of French Barouqe and therefore is better suited to the comparison with Versailles, though it is in no way nearly as big or impressive.

Personally I hate it when places have to be described as Denmarks Versailles or the Venice of the north/south/etc or the Paris of the east/west etc etc. To me it suggests that these places are inferior knock offs of famous places.

Thanks Morten.
I see from visitdenmark.co.uk that at Fredensborg Palace “The royal private garden, the Orangey and herb garden are located adjacent to the castle. They are open for the public in July, as are parts of the castle and the chapel. The surrounding castle gardens are open to the public all year around and admission is free.” Assuming a July visit, in your opinion, is there time in a single day trip from Copenhagen to see Frederiksborg Castle, whatever parts of Fredensborg Palace are open for viewing, and then Kronberg Castle? Or is that really too much to do in one day without almost running through the locations? Thanks. BTW, I’m with you on comparisons like “Versailles of Denmark” etc. I only used the term because it added to my confusion as to how many locations I was looking at.

We went to both Fredericksborg in Hillerod and Kronborg, did them on separate days, and did not go to Fredensborg. The day we went to Hillerod, we got an early start from Copenhagen, spent plenty of time at the castle, had lunch in Hillerod, then returned to Copenhagen for the afternoon. The day we went to Koronborg in Helsingor, we also went to the maritime museum, and then on our way back to Copenhagen, stopped at Humlebaek to go to the Louisiana Museum of Modern Art (which is stunning). If you only do Fredericksborg and Kronborg, I think those two can be done in a day (and I believe there is a train that runs between Hillerod and Helsningor. I don't think adding Fredensborg is really feasible to add as a third stop in that day, unless you really want to just fly through each stop. How many days are you there?

Still planning, but first guess is we will be in & around Copenhagen for at least 4 days, not counting the day we arrive from Iceland. Maybe more days if we identify enough high priority sights to stay longer. Thats why Fredensborg piqued my curiosity. Thanks.

Fredensborg is located on the train line between Hillerød and Helsingør.
Frederiksborg, Fredensborg and Kronborg would be stretching it a bit for one day if you want to do the tours there, and not just peak at the them from the outside. Especially since Helsingør has more to offer than just Kronborg, there is also the charming old town and the excellent Maritime Museum and also Louisiana Museum of modern art in Humlebæk on the coast on the way back to Copenhagen.
If you want to see all these sights, do it in two days.