Water vs Twater (Externalism, Internalism)

I’ve been reading some pages in Stanford Encyclopedia of Philosophy about externalism vs internalism and I’m struggling a bit to grasp the real issue.

Note: I’m not an academic or trained in philosophy so please be patient with imprecise language and/or thoughts.
Water vs Twater:
One example related to externalism vs internalism provided in the Encyclopedia is twin worlds with identical people and the only exception is water=H2O on one planet whereas water=XYZ on the other planet. The fact that the people from the two planets use the same word for something that looks and acts the same but is actually different implies <???something philosophical???>.
My simple view of the brain says that it doesn’t really matter that they refer to two things that are different under the covers. If I’m trying to build some artificial intelligence, all I care about is creating the ability to compress and map the input into some form that can be used effectively to produce behavior that succeeds in that environment. That compression and mapping process is generally imprecise and the water/twater example seems like it is just another example of that imprecision.

What am I missing?

Is there something that the water/twater example exposes that would influence our understanding of how the brain/mind works?