T-15
On the Aechmea fasciata [Silver Vase],the pups will usually flower in 2-3 years,when about the size of your original mother plant.
The other plant you describe sounds like a Vriesea,and you can comepare yours to the photos that can be found on a very good bromeliad web site : WWW.FCBS.ORG
Also, plenty of other growing information there too.
Bob

The time to flowering will vary according to what conditions the pups are given, and sometimes a plant will send off pups and die without flowering. I had this problem until I moved to New Orleans, put them outside nearly year - round and allowed them to experience the change of seasons. Whether it was the increased sunlight or varying temperatures, they then bloomed easily for me.

I agree, the other plant sounds very much like a Vriesea. Vrieseas prefer more humidity and less light than is necessary to keep Aechmea fasciata happy. They are easy to bloom, most blooming in wintertime.