Tag along, but what is the relationship between the Wenceslas in the carol and the St. Wenceslas of the Catholic Church?

The answer to your questions would appear to be "both", in a way. Wenceslas of Bohemia has long been venerated as a saint and noted for his charity and piousness during his life - and especially after his death. Not just in his native land either, as evidenced by his martyrdom and canonization, although that is of course where his cult has been most prominent by far.

In the history and legends of Bohemia, Wenceslas' role is actually twofold. Not only that of the aforementioned pious and goodly saint, but also as a legendary ruler of the Premyslid dynasty - indeed he has been the patron saint of Czech lands for centuries now, and is the mythical "king in the mountain" that will ride out from the Blaník mountain with his knights when his nation needs him the most in the local version of the popular myth.

However, his image of a saintly ruler has been sort of inflated over the following centuries, hence the weasely answer. That being said, while I do not know the motivation behind John Mason Neale's choosing of Wenceslas as the subject matter in his lyrics, what writings we have about the duke do portray him in a similar light as the carol even if we discount the most exaggerated hagiographic accounts.

At some point between 921 and 925 Wenceslas became the duke of Bohemia and focused on maintaining peace and stability in his lands as opposed to territorial expansion. His foreign policy was also one of avoiding conflict, leading to Bohemia paying tribute to Henry the Fowler of Germany in exchange for peace.

Incidentally these policies would also prove to be his undoing, as his ambitious brother Boleslaus had Wenceslas killed around the year 935 and took the throne for himself. He then reversed his predecessor's policies and became an active and aggressive ruler – and funnily enough quite successful and strong as well.

In addition to striving for peace, Wenceslas' rule was also marked by noticeable religiousness and a good relationship with the Church. As a boy he was raised by his grandmother Ludmila (who would also be later canonized), a pious woman whose faith would influence Wenceslas' upbringing and education that included the reading of religious texts.

Furthermore, following Wenceslas' submission to Henry the Fowler, the Bohemian duke received a relic of St. Vitus (the remains of his hand) from the German, and built a church in Prague dedicated to the saint – the third church to be built there in a fairly short period of time, suggesting a high degree of importance. The present day St. Vitus Cathedral is built in the same place as the 10th century rotunda.

After his murder in 935, it only took a very short time for a number of works to appear, praising the Christian qualities of Wenceslas. Crescente fide, Legenda Cristiani, the First Old Church Slavonic legend, the legends of Laurentius and Gumpold, and The life of St. Wenceslas are all 10th or early 11th century writings extolling his saintly virtues, and ascribing to him all manner of deeds ranging from the believable – founding of more churches, acts of charity to the poor – to those less so, such as planting vineyards for the sole purpose of making sacramental wine or uprooting pagan idols – or even outright miracles with angels and shining crosses appearing next to him.

So yes, although most of what we know about Wenceslas is obscured or augmented by the legend surrounding him, it does appear that Wenceslas possessed at least some of the qualities of a good, pious Christian, enough to warrant respect and veneration basically immediately after his death.

According to Gerry Bowler's The World Encyclopedia of Christmas, there is no connection between Saint Wenceslas and the King Wenceslas in the carol. He also references that he is " 'a sleeping king'... who will one day rise again when his nation needs him most". (246) Perhaps this is why J. M. Neale selected him?

Bowler, Gerry. The World Encyclopedia of Christmas. Toronto: McClelland & Stewart Ltd., 2000.