In terms of differences, eukaryotic cells are much larger and more complex than prokaryotic cells. On average, a typical eukaryotic cell is about 1,000 X larger in volume than a typical prokaryotic cell.
This means both drugs (amoxicillin and penicillin) can treat a wide variety of infections. However, unlike amoxicillin and penicillin, the routinely prescribed drug, metronidazole, has a more selective action towards anaerobic bacteria. These bacteria are the ones causing the signs and symptoms of bacterial vaginosis.
Antibiotics kill bacteria, not archaea, fungi, or protists. The discovery of the antibiotic penicillin in the 1920s made a big impact on human history. Not only did it lead to a cure for bacterial infections that were once deadly, but it also led a big interest in finding new antibiotics.