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.
The story of penicillin - the first antibiotic used successfully to treat people with serious infectious diseases - begins with a bit of luck. Alexander Fleming, a British scientist, noticed in 1928 that mould had prevented the growth of bacteria in his lab. But the main plot of the story involves the rediscovery of penicillin 10 years later by an Australian scientist born one hundred years ago this year.