They are most likely related via her mother Lady Emma Cavendish, whose father was the Duke of Devonshire. One of the previous Duchesses of Devonshire was born Georgina Spencer (daughter of the first earl Spencer). However, not sure if that's a fourth cousins once removed-relation. I wouldn't be surprised if there are other links as well.
Edit: the line for each of them to John Spencer, 1st Earl Spencer: in this lineage they would be 5th cousins twice removed.
Stella Tennant - Lady Emma Cavendish - Andrew Cavendish, 11th Duke of Devonshire - Edward Cavendish, 10 th Duke of Devonshire - Victor Cavendish, 9th Duke of Devonshire - Lord Edward Cavendish - Georgina Howard, the Countess of Carlisle (born: Lady Georgina Cavendish) - Georgina Cavendish, Duchess of Devonshire (née Spencer) - John Spencer, 1st Earl Spencer
Lady Diana Spencer - John Spencer, 8th Earl Spencer - Albert Spencer, 7th Earl Spencer - Charles Spencer, 6th Earl Spencer - Frederick Spencer, 4th Earl Spencer - George Spencer, 2nd Earl - John Spencer, 1st Earl Spencer