I would call it a half-height glass separation or partition.
The pinterest image you showed was found using those keywords
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
I've seen the following two, though they may be technically wrong:
- Glass Banister
- Glass Balustrade
I would call it a "wood-framed glass railing". If it were outdoors, I might call it a "wood-framed glass fence".
If the top edge of the railing/fence were glass (instead of wood), I would just call it a "glass railing".
Actually, this is simply a part of the glass railing system. Basically, a glass guardrail. You can often see these in malls and supermarkets, and in office buildings.
My personal thoughts: People may mistakenly think it's a half wall or a partition wall but it's not. It doesn't split, separate or divide the room. It doesn't enclose an area within a larger area. Notice that it isn't standalone unlike half walls or partition walls, it is a combination of two guardrails creating a railing system.
What you see here is just a kind of a glass railing system with the handrail made of wood and with rather wide glass panels. The guardrail on the staircase is also a part of the glass railing system. You can google for "interior glass railing systems" and you'll find a lot of examples.
Here are a few examples of such interior glass railing systems: