I don't see a list of common terms used by the Immersive Daydreaming Community, so here are my personal terms. If you like, you are welcome to use them.
Community terms I have seen:
-Paracosms- Highly developed inner worlds made from imagination. Tend to start from childhood but last a lifetime for some people.
-Author, Creator, Brainstormer, Daydreamer- Refer to a creator of a Paracosm or Paras.
-Paros/Paras, Imaginary Friends, Characters, OCs, Denizens- Terms to describe created imaginary entities or characters. They can be either interactive or story-based characters.
-Veritbond, Verit- Term from Foxglove-Burning's post on Verits. Paras sharing a very deep connection with their creator. So for the context for my paracosm blog, verits would be my most active interactive paras.
-Immersion/Dreaming/Daydreaming- To describe diving into the Paracosm for a period of time.
My personal terms in relation to my paracosms:
-Set-Pieces, landmarks, Settlements- Refer to created areas within a Paracosm like cities, villages, dungeons, or ruins. Also include areas in unpopulated lands and territories.
-Pocket-Sentience- Refer to how paras use a small portion of their creator's sentience to communicate and stay active with and without their input.
-Lore/Story-Sentience- Refer to how characters within a Paracosm who are not aware of their Author's existence and mostly rely on the rules of the Paracosm for function, communication, and activeness.
-Bandwidth- To describe how much mental work to keep up with Paras, Paracosms, and other imaginary constructs.
-Brainstorming/Tinkering/Worldbuilding- Paracosm management like currency, conlangs, environment upkeep, para group relationships, politics, conflicts, inventory checks, and concept test-builds. Mostly checking on important things in a paracosm that is heavily structured or story-driven.
-Present/Being Present- To be awake and present outside the paracosm.