White hunting terriers from England go by many names and, depending on the country, the names do not even mean exactly the same nowadays. There are Parson Russell Terriers, Jack Russell Terriers, Foxterriers and, to make it even more confusing, Parson Jack Russell Terriers, all of which go back to the same ancestors.
It was the Reverend John "Jack" Russell (1795 - 1883) who started breeding such dogs systematically for working purposes. The breeder of my dogs, an old man in Wales who breeds them since he was a boy just for his own working purposes and sells the rest, calls them "Russell Terriers", which is, I think, a fair way out of the dilemma, specifically if one isn't bothered with standards (beautiful is who beautiful works) and memberships.
The white terriers have caught the attention of many artists. That is, I presume, at least partly because their short hair allows full view of their facial expression, something their long-haired brethren naturally don't share. A judicial look (dirty by any other name) from one of them is priceless. Add their natural cheekiness and showmanship, their zeal when working and their appreciation for the good life at home and one has found the ideal objet d'art.
Many pictures, specifically from the Victorian period, are chocolate boxy, some are just plainly descriptive and unexciting, but some get it just right. This is a random collection of pictures I like and the order doesn't imply any assessment whatsoever.
"Gamekeeper's Companion" by John Fitz Marshall (1859 - 1932)
"Terrier in a Landscape" by William Elsob Marshall (1859 - 1881)
"Two Fox Terriers" by Alfred Wheeler (1852 - 1932)
"Jocko with A Hedgehog" by Sir Edwin Landseer (1802 - 1873)
"Bay Horse and White Dog" by George Stubbs (1724 – 1806)
So here we see a white terrier well before the age of the Reverend John Russell.
"In the Lap of Luxury" by Philip Eustace Stretton (1865 - 1919)
"A Nest of Dogs" by Sir Lawrence Alma-Tadema (1836 - 1912)
I have added the last picture because Alma-Tadema seems to be such an unlikely painter of dogs, at least of dogs that are not heavily stylized. They may even not be terriers (my bet is on a Spaniel breed), but the picture is too special to be missed.
"The Intruder" by Arthur Wardle (1860–1949)
Russell- or Fox Terriers with (presumably) an Irish Terrier.
And just for a reality check and to show how little has changed over the centuries:
Jill 2006, with her litter by Jack
Centuries of "handsome is who handsome does" breeding has kept the breed healthy, vital, efficient -- and largely the same.
And for good measure, some newer paintings with other terriers:
"Bordeaux Terriers" by Paul Doyle. (They are Border Terriers, of course.)