Its not so much style of play , but style of BANJO ! Tenor (Four String) is a totally different instrument to Five String !
Tenor (In Folk) tends to be Single string Melody , especially for Irish (As Barney McKenna of the Dubliners , whereas Five string is more picking , either Old Timey or Bluegrass !
I have had guys sent to me from a local shop for Banjo Basics who had bought a Five String and wanted to play Irish !