The Wagenfeld vases aren't cased. and as such are the same colour all the way through. Wagenfeld vases of that range are generally a rauchtopaz colour, which is to say a smoked grey/brown, rather than purple-tinged. Also, the bases on the WMF vases aren't as rounded as yours.
I personally don't think they're closely related. Perhaps kissing cousins, at best.
Your vase looks very 60s/70s to me, and the small hole at the top isn't an uncommon feature in both European and Scandinavian glass.
But these are just my opinions, and I may be wrong. It's frequently been known to occur. :lol: