Not exactly a replacement, as the tuning, although equivalent in terms of pitch class, is an octave below that of the madolin or fiddle (or violin, for that matter). But since the size of the instrument makes it possible to tune it in fiths, as explained by Scott in his answer, it makes of course all the sense to tune it in a way that can be immediatly played by those familiar with these instruments.
In fact there's a whole sub-family of banjo like instruments that share a tuning in fiths, the most relevant being:
- The most close "cousin" of the tenor banjo (in terms of tuning only, as it has 8 strings and not 4), would be the mandola, a larger version of the mandolin tuned an octave below.
- A four 4 strings banjo tuned like (in the same ocatve range of) a violin would normally be called a banjolin. There has been fretless banjolins too, but they are rare.
- The 8 stringed mandolin-banjo was very popular throughout Europe in the first half of the 20th century, yes, as a direct louder replacement of the mandolin.