A pony wall is a short wall. In different circumstances, it may refer to: a half wall that only extends partway from floor to ceiling, without supporting anything. a stem wall, a concrete wall that extends from the foundation slab to the cripple wall or floor joists.Wikipedia
Hmm. In America, if you refer to water in a "glass" people will normally understand you to mean a container made of glass. Drinking containers made of other materials are typically called "cups", or if they are tall, "tumblers".
Of course if you are at a friend's house and you ask for a "glass of water", he may give you the water in a plastic tumbler. But I don't think that that's really because he thinks of the plastic tumbler as a "glass", but just because he thinks this is an acceptable substitution. Like if you said, "Do you have another chair?", he might bring a stool or a bench if that's all he has.
When someone wants to make clear that they mean a real-live glass and not a metal or ceramic or plastic or whatever drinking vessel, it's not uncommon in America to say "a glass glass" or "a real glass".
Of course you specified "India", so this answer may be entirely irrelevant. :-(
Best Answer
I would call it a half-height glass separation or partition.
The pinterest image you showed was found using those keywords
Interestingly enough so was Pony wall and Half wall