Parametric Prancing and Polar Dancing

When creating the parametric plot


My three apps Goodgrapher Pro, PocketCas and QuickGraph+, together with Wolfram Alpha all give me the same result -luckily and not unexpected.

Wolfram Alpha
GoodGrapher Pro

However, asking for a spherical plot


gives me two different outcomes in GoodGrapher Pro and QuickGraph+

GoodGrapher Pro

Hmmmm, QuickGraph+

The second is a weird one, but luckily a beautiful one as well. I can’t find out where the difference comes from.