Vector Parametric Plot different from polar plot using norm of vector

I’ve defined two vector functions (2D) of real variables and then I plotted them parametrically using ParametricPlot[]. The result is the green and orange curves (the blue curve is a reference circle).

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What I’m seeking however is the norm of theses functions, and I was getting weird values from the norm – so I decided to plot the resulting norm parametrically where I plotted {Norm1[u] Cos[u],Norm1[u] Sin[u]} and {Norm2[u] Cos[u],Norm2[u] Sin[u]} (u going from zero to $ 2\pi$ . Here Norm1 and Norm2 are just the Norm[] method applied to the vector functions. I get this funky plot that doesn’t match the vector plot.

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I cannot disclose the functions themselves as they are an on-going group work but they are functions of real variables. It seems very strange that taking the norm and then doing a polar plot like that does not recover the original plot. Any thoughts or pointers on what could be happening?