Tá an fhuinneog ar oscailt
The window is open

an bhfuil sí dúnta
Is it shut?

Can somebody explain to me the difference? Arn't oscailt and dúnta the same "form" of different verbs? (I think they are the verbal noun here....)

No. oscailt is the verbal noun of oscail, and dúnta is the verbal adjective of dún.

You can say Tá an fhuinneog oscailte. as well. I think of ar oscailt like "ajar" as in it describes the state only and not the result of an action, which oscailte implies.

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[hr]Múinteoir Gaeilge - Irish Teacher[/hr]
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Verbs: dún and oscail.
Verbal adjectives: dúnta , closed, and oscailte , opened - without prepositions
Verbal nouns: dúnadh and oscailt - with prepositions (ar oscailt, ag oscailt, chun oscailt)

While there is ar oscailt, "(being) open", the counterpart ar dúnadh, "(being) closed", would be very unusual.
Usage of preposition ar + verbal noun is not very productive.