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Is there any distinction between these two? I couldn't find anything in google under "Adaptive vs progressive mesh", but googling them both separately gives results as if they were likely the same.

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Definitions:

Progressive meshes: This method involves the saving of mesh as a collective structure which contains several copies of the same mesh in different LOD. In this technique, the whole of the mesh is made into one with lower resolution.

Adaptive meshes: Rather than enumerate the huge number of polygons that would be required to get an accurate discrete approximation of such a complex shape, mesh refinement techniques split the surface representation into a coarse polygonal mesh combined with a continuous displacement function. This means that you get different LOD/resolution while rendering the same mesh in the same frame according to the distance from the camera. Here's an example of Adaptive Meshes:

enter image description here

As you can see here in this image, the mesh is tested on each vertex for the distance from camera/ depth into scene. the portions of the mesh which are closer to the camera are rendered with high detail, while those portions away are rendered with low detail. In contrast to this,

enter image description here

Progressive meshes, like in this elephant image, change the whole mesh at once when the distance from camera changes.

Thus to summarize, Progressive meshes change resolution of the whole mesh whith distance from camera and adaptive meshes change only part of the mesh's resolution with distance, so the same mesh can have different Levels Of Detail in the same frame.

Hope that helps as a basic difference.

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