http://en.wikipedia.org/wiki/Ursula_Pole
http://en.wikipedia.org/wiki/Arthur_Pole_(1502–1535)
http://en.wikipedia.org/wiki/Arthur_Pole_(1531–1570)
Arthur and Ursula are just "Pole", and I suspect you're thinking of the second Arthur Pole (son of Geoffrey Pole, who in turn is the brother of Ursula Pole and the first Arthur Pole) rather than Ursula's brother Arthur who died in 1535.
The just-plain-Poles are the senior descendants of
George, Duke of Clarence, younger brother of Edward IV and older brother of Richard III. There's also a de la Pole family, who are (confusingly enough) also York pretenders, but the similarity of names is just a misleading coincidence.
The de la Poles are descended from a sister of Edward IV, George of Clarence, and Richard III.
John de la Pole, 1st Earl of Lincoln named by Richard III as his heirs if he died without surviving issue (as indeed he did) in preference to the genealogically senior surviving children of the Duke of Clarence (presumably because Clarence's children were still minors, or because Clarence had been executed for treason against Edward IV). John never pressed his claim, although he did support a rebellion figureheaded by an impostor claiming to be the son of the Duke of Clarence. John was executed by Henry VII, and after his death two of his brothers in turn (
Edmund de la Pole and Richard de la Pole) did advance claims to the English throne based on Richard III's will. The latter,
Richard de la Pole, at one point assembled an army of 12,000 in Brittany to invade England but was unable to find a way to cross the Channel. After Richard's death, his claim passed to his daughter Marguerite de la Pole, who married into a French noble family and presumably made no attempt to press the claim.