There are basically 2 different types of 4-string banjos:
1. The Tenor 2. The Plectrum
The Tenor banjo has a scale neck that is shorter than a 5 string and is most often used in Irish settings today. They are normally tuned in the traditional CGDA sequence from low to high strings. Some Irish Tenor banjo players use the octave tuning of GDAE.
The Plectrum, however, has a bit longer scale neck closer to the length of a 5-string banjo. These banjos have been used more often for pop standards and ragtime music in a more Dixieland setting.
Generally, the Plectrum and the Tenor are rarely used in Bluegrass settings. Four string banjos also do not have a drone string and are most generally played with a flatpick.
The type of banjo you will want to purchase will be largely dictated by the style of music you want to play. This may determine whether you want a 4 string or a 5 string. You will probably want a 4 string banjo if you are wanting to play Jazz or Dixieland style music. For Celtic and Irish styles or country and bluegrass, you'll want to look for tenor banjos and 5-string banjos respectively. Although it is possible to fake playing Dixieland on a 5 string by using only the bottom 4 strings, it is nearly impossible to get a 5 sting sound on a 4 string banjo.