plotting – 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).

enter image description here

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 $2pi$. 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.

enter image description here

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?