Hello from Stockholm - my hometown 🤩
You are absolutely right, there are two cruise harbors in Stockholm (and even a third one in the city of Nynäshamn - 60 kilometers/1 hour south of Stockholm):
The two are the 2) Stadsgården (Masthamnen) and the 1) Frihamnen. See the map.
It’ corrrect - according to the schedules of Stockholms Harbours homepage - that MSC Poesia will berth in the harbour of Frihamnen 2).
(This may have to do with the fact that the Stadsgården is more popular due to the geographical location and even the lack of capacity as there is only space for one or two cruise ships...and therefore it - probably - is more expensive for the cruise line shipping companies to berth there.
Stadgården 2) is a bit more centrally located and within a walking distance of about 30 minutes in to the Old Town and the central parts of Stockholm (the location of the harbor is even much more attractive when it comes to having a very nice view overlooking the inner parts of the city).
The Frihamnen 1) is about 60 minutes away (by feet) from the city center; it's a bit in the middle of nowhere and the closest surroundings are boring. MSC usually has transfer buses going in to the city center - however, not without a cost (I've never experienced that MSC freely will give away transfers/transports. The cost used to be USD/Euro 10 per person...nowadays I don't know).
A taxi (up to 4 passengers per ordinary car) may be an alternative. However - always check the price with the driver before you enter the taxi...regrettably there are many tourists being cheated due to many quite unserious taxi companies/-drivers (the market/-competition is free here).
You say that your plan is to go to “Djurgården” (which is a very nice recreation area with parks, entertainment facilities (such as the tivoli ”Gröna Lund", a large folklore museum (i e the ”Skansen”)...even with some animals, the ABBA museum, restaurants, etc).
My personal favorite is to discover the island by a (rented) bicycle...it's georgious to bike along the coastline of the island of Djurgården.
There is even a tramway - often run by quite old wagons - running from the city center to Djurgården.
You'll see Djurgården at the map...and the ABBA museum is located next to where it says "Gröna Lund" (which is the tivoli).
Hopefully you will have a very nice stay here in the capital of Sweden. I believe for sure you will enjoy it; especially the green areas and water sorrounding ”everything”.
The archipelago is stunning; arriving / departing on board a cruise ship normally takes around 5 hours from the first islands at open sea in to the city centre. Enjoy! 🛳️
Happy journey and bye-bye 🙂
(FYI, I was employed for 12 years at MSC Cruises' Sweden office as a Key Account Manager (responsible for travel agencies and tour operators in Sweden) and have cruised onboard - among many other other vessels belonging to MSC as well as other cruise shipping companies - MSC Poesia).