According to a Guernsey legend, St Samson of Dol arrived in Jersey but encountered such a hostile reception in the then-pagan island that he moved on to Guernsey. The welcome being much warmer in Guernsey, he repaid the inhabitants of that island by sending all the snakes and toads from Guernsey to Jersey.
However, the origins of these terms possibly goes back to the 17th century and the days of Press Gangs. The Channel Islands had some British Government immunity, but attempts were still made. The British Governor of Guernsey had famously remarked that there were plenty of idle men - like the numerous donkeys in and about the streets. This was used later in Jersey, that the idle men were as numerous as the toads about the Samares and Goose Green marshes.
There is another reference which lends weight to this theory. Press gangs did visit both Jersey and Guernsey in the Parliamentary era, yet strangely the authorities in Guernsey, which supported the Parliament, put up more resistance than did those in Royalist Jersey. Perhaps it was because Jersey had had a Parliamentary regime forced on it. Nevertheless, the press gangs did not have an easy time of it in Jersey and those resisting being pressed were attacked both by the Governor's troops and the press gangs. In one incident one inhabitant was killed and others wounded when the troops opened fire.
In St John one soldier shot and killed Francois Maret, who resisted arrest, and then others cut down his fellow parishioners with swords. The Governor allegedly inquired of the soldiers afterwards whether they had killed toads.
There is another entirely different theory, and that is that the name does not originally derive direct from the French for toad, but from de Crapoudoit, the name for one of the three districts into which Jersey was divided for administrative purposes back in the 12th Century. Crapoudoit is thought to have consisted of the four western parishes of St Ouen, St Peter, St Brelade and St Mary, although the parishes may not have existed as such at the time the island was first split into three divisions, or Ministeria.
The eastern part of the island was called de Gorroic, an early spelling of Gorey, which must have been at its centre, although it is doubtful if it was inhabited as a village at that time. The central part of the island was de Groceio and the part to the west of what is now St Peter's Valley, de Crapoudoit. The brook running down the valley was called Crapedoit, the brook of toads.
If those people living in the west of the island were known as Crapedoits, this could easily have been corrupted to Crapauds, particularly by those Guernseymen with whom they came into contact while fishing between the islands, and the name may have come to apply, at least in the minds of Guernseymen, to all inhabitants of the larger island, much earlier than is otherwise supposed.
The issue is confused even further because Crapedoit is also the name of a fief, which became part of the Fief de Samares (it's not a coincidence that until the 17th century, the area was a marsh). There is also an ancient Jersey surname de Crapedoit. Did they come from the west or the fief?
Donkey on the quayside
Another legend has it that some Jersey seafarers, after an evening in a St Peter Port hostelry were going back to their vessel to set off on the tide for Jersey. On the same quayside was a Guernsey vessel that they knew was also to go to Jersey.
Donkeys were often used at the time to pull carts. One such poor creature had expired during the day and the body was still on the quay, maybe waiting till morning to be disposed of. The Jerseymen thought it a good joke to lever the donkey's body into the water and tie it the rudder of the Guernsey boat.
Back in Jersey, to the amusement of the Jersey sailors, the Guernsey boat eventually arrived, having taken some twenty four hours instead of the normal six or seven hours for the journey - the Guernsey men shaking their heads as to the slowness of their boat.
The less palatable version of the same story
(As told in The Revenge of the Channel Island Joke Book) The dead donkey was attached to the rudder of the Jerseymen's boat by the Guernseymen, meaning that the Jerseymen suffered a long and arduous crossing.
Determined to pay back the Guernsey folk with interest, the Jerseymen had their wives skin the donkey, turned the flesh into pies, and served it to les ânes the next time they met. Revenge was that much sweeter when the Guernsey folk complimented them on the excellence of their cooking...!
More recently the term 'Bean' has become common parlance to describe a Jerseyman, but it is not something which true Jersey people would accept as an alternative for crapaud. It has its origin in the island's 'national dish', the Jersey bean crock, and it is probably something which was invented by newcomers to the island as a derogatory term based on their hosts' perceived lack of culinary expertise.
However it originated, it is not something which is based on any inter-insular rivalry.