I don't know what makes you think that fear would mean a dog isn't a Jack Russel. I've actually met a lot of fear aggressive Jack Russells. Also dogs' voices can vary in pitch and tone just like human voices. Some breeds do have a distinctive bark but that's not the most distinctive thing about them.
That other dog is either a JRT, JRT mix or Rat Terrier/Rat Terrier mix. We were actually just having a discussion on another thread about how JRTs can have very varying appearances. But the docked tail does make me think she's more likely a Rat Terrier.