Hi, and welcome! The widgets aren't really behaving differently — they're showing each shape's own corner radius, which is stored with the shape.
A couple of things explain what you're seeing:
• The widget sits along the edge at a distance from the corner equal to the current radius. So if the light purple rectangle already has a larger radius set, its widgets start further from the corners than yours, and dragging them produces a bigger curve.
• A corner radius can't be larger than half of the rectangle's shorter side. Your rectangles are very shallow, so on your new one you reach that maximum very quickly — the two corners on each short end meet and the end becomes a semi-circle. Dragging back to zero gives you the hard edge again, which is why it feels like all-or-nothing.
To copy the light purple one exactly, don't drag by eye: select it, double-click one of its corner widgets (or open Window > Transform) and note the Corner Radii value, then select your rectangle and type in the same value. Also check the corner type matches — Alt-click (Windows) / Option-click (macOS) a widget cycles between Round, Inverted Round and Chamfer.
There's a good overview of live shapes here: https://helpx.adobe.com/illustrator/using/live-shapes.html
Hope that helps!
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