1. She is at the river.
2. She is by the river.
3. She is at the car.
4. She is by the car.
5. She is at the table.
6. She is by the table.
7. She is at the computer.
8. She is by the computer.
[Is each pair the same? Is there any difference in each pair?]
Each pair is pretty much the same in meaning, yes.
The word "by" suggests she's right next to the river or car or table or computer. The word "at" could mean she's in the near vicinity of each one, if not right next to it.