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Do they mean the same? Or different things?

For example, are the people at the back of this picture sitting at the glass wall? Or by the glass wall?

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Example sentence:

While eating at the cafeteria, I spotted eyes peering at me. They belonged to a man sitting at/by the glass wall.

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Sit at is generally used when you're referring the place/area where someone is, like in:

He sat at the airport waiting for his flight. He sat around at home doing nothing.

Sit by means:

Sit near or at the side of:

A small child was sitting by her side.

In your sentence;

.... They belonged to a man sitting by the glass wall.

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at can also imply "facing" whereas by can imply either a sideways orientation or simply proximity.

The mountaineer was sitting at his fire.

Grandma was sitting by the fire, knitting booties for her granddaughter.

Many speakers might use by even if Grandma was close to the hearth and facing the fire. But few would use at if Grandma was sitting sideways relative to the hearth, only her right or left side getting warm, or if the fire was at her back.

Where in the cafeteria are you?
-- We're sitting at one of the tables over at the window.

There, the second at refers to the position of the table relative to the window, and the first at refers to the position of the speaker relative to the table.

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It's nothing to do with sitting. Prepositions are often governed by a particular verb or adjective, but in this case, it's their primary locative sense.

At tends to imply more than just physical location: either that the person is there for a particular purpose ("sitting at the table"; "waiting at the checkout") or that the place is distinctive, and saying it defines where the person is ("at the corner"; at the London Eye").

So if you said they were sitting at the glass wall, it would either suggest that they were doing something with the wall (may be they'd sat there so that they could look through it), or that the glass wall was a landmark you expected your hearers to know.

By doesn't have these connotations, so that would be the normal choice here.

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