They are not necessarily the same if the discount store doesn’t offer the same options. A few cheap places don’t offer ultra high refractive index lenses. With the standard high index lens my lenses are very thick at the edges. Also, not all discount stores offer the same anti-scratch, anti-glare, or photochromic options.

The lenses that you get from a discounter will match your prescription, but expensive shops can have differentiating features.

As places move to outsourcing their lens production they can offer more products, since they aren't physically doing it in-store. The handful of discount "while you wait" places, do indeed, have more limited options but it is fast.