Robots are frequently tasked to gather relevant sensor data in unknown terrains. A key challenge for classical path planning algorithms used for autonomous information gathering is adaptively replanning paths online as the terrain is explored given limited onboard compute resources. Recently, learning-based approaches emerged that train planning policies offline and enable computationally efficient online replanning performing policy inference. These approaches are designed and trained for terrain monitoring missions assuming a single specific map representation, which limits their applicability to different terrains. To address these issues, we propose a novel formulation of the adaptive informative path planning problem unified across different map representations, enabling training and deploying planning policies in a larger variety of monitoring missions. Experimental results validate that our novel formulation easily integrates with classical non-learning-based planning approaches while maintaining their performance. Our trained planning policy performs similarly to state-of-the-art map-specifically trained policies. We validate our learned policy on unseen real-world terrain datasets.