I've compared my tall one & small one - they are basically exactly the same dimensions & profile, i.e. if you lopped c. 3" from the tall one, you would have the small one. So it would suggest that if the tall one is
Tamara Aladin, then the small one would be too.
With that designlasi website you get more info if you register, but there's no reference given for their attribution for the tall vase.
Andy McConnell does say that there are a few designs which don't appear in any Riihimäki catalogue & also that some designs are unillustrated in any catalogue.
I'd love to see this 1976 export catalogue. It's been mentioned so many times