Fans of the former tend to downplay the significance of their meetings while their counterparts in Perth maintain that they qualify as derbies.
Debate will continue for as long as the Tay flows between the two cities. There is, however, one thing which both parties will find it nigh on impossible to disagree about since the evidence was plain to see in a truly awful goalless stalemate between the sides on Wednesday night.
They are united in an unseemly scrap for top-flight survival. It is becoming a rather more serious issue than joshing about the difference in the way they perceive each other.
Dundee, who already have the unwanted honour of most relegations from the top flight since 1975's league reconstruction, can ill-afford another one.
St Johnstone are in an unusual position where they probably can afford it with money in the bank after recent player sales combined with trophy successes. It’s the humiliation of seeing things go south so quickly that will smart.
The one meeting between the teams still outstanding in this campaign – at Dens Park, sometime in April or early May – is likely to prove critical to both club’s future prospects.
Derby or otherwise, it has the potential to be the most critical game between the sides since a final day shoot out at Muirton Park in 1962. Dundee needed a draw to win the title and St Johnstone required a point to stay up. The visitors triumphed 3-0 to lift their sole Scottish title. A St Johnstone side including Alex Ferguson in its ranks slid into the second tier.
Both clubs know the pain of exile from Scotland’s top table though the agony will seem particularly acute in the case of St Johnstone should it come to pass.
One of only two clubs outwith Rangers and Celtic to lift a cup double in a single season, they will have the ignominy of being the only side to then be relegated 12 months later all to themselves.
Even their current position of bottom place is a staggering fall from grace. The home draw with Dundee, acceptable in the circumstances if not enormously helpful, leaves Callum Davidson's side still two points adrift of the 11th place Dens Park side.
“The pressure is the complete opposite to what we were used to last season,” explained left back Callum Booth after the 0-0 draw with Dundee.
“It’s a different pressure. But then there’s always pressure when you play football. Once you cross the white line you just focus on your performance and try not to think about the noise with the run we are on. Hopefully this is the first step to us building our way back up and away from the bottom.”
The trouble is that steering away from difficulty is looking a tall order for both clubs.
Results have conspired against them. St Mirren’s win over Aberdeen relieved their worries slightly. Dundee United’s defeat over Ross County keeps the Dingwall side in touching distance but stems the Tannadice’s side’s series of league defeats.
Dundee entertain St Mirren this weekend knowing that a win is vital in an ultimate six pointer. St Johnstone, meanwhile, travel to face Aberdeen.
There are few certainties but the likelihood of a private relegation battle continuing to develop between two old enemies – if that’s how we can term them – seems almost guaranteed.