The concept of Alpha parameters (in the context of alpha shapes)

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Please clarify the concept of Alpha parameters.
A simplest non-degenerate example computing alpha shapes, possibly just with 3 or 4 points would help.

The following sources seems to have conflicting information. Are two conventions prevalent in literature?

Source 1:
https://alphashape.readthedocs.io/en/latest/readme.html#using-a-varying-alpha-parameter When the alphashape function is called with an alpha parameter of 0, a convex hull will always be returned.

Source 2: https://doc.cgal.org/latest/Alpha_shapes_3/index.html#Alpha_shapes_3Definitions Hence, the alpha shape becomes the convex hull of S as α→∞.

Source 3: https://www.clear.rice.edu/comp651/papers/Edelsbrunner-AlphaShapesOnShapeSetPointsPlane.pdf As α approaches zero, the alpha-hull approximates the common convex hull.