I'll enlarge a bit on what Phil said. It's not uncommon for a rose variety to produce a spontaneous genetic mutation--a 'sport'. The rose produces a branch with characteristics that are different from the rest of the plant; if the mutated growth is desirable, a new variety can be propagated from it by taking cuttings or buds.
There are different kinds of sports.
The flower color can change: David Austin's 'Mary Rose', with pink blooms, sported to produce 'Winchester Cathedral', which is white; the Tea rose 'Safrano', soft buff-peach-parchment, sported to 'Isabella Sprunt', pale lemon yellow; Rosa gallica 'Officinalis' sported to produce the striped R. gallica 'Versicolor', also called 'Rosa Mundi'. In all these cases, aside from the color, the sport is identical to the parent plant.
A bush or shrub rose can sport to a climber. Usually climbers are less remontant than their sport parents. Generally, as Phil said, the climbing offspring is called by the same name as the parent, with the word 'Climbing' added, as in 'Climbing Cécile Bruenner' or 'Cl. Etoile de Hollande'. There's at least one case of a once-blooming climber sporting to a repeat-blooming shrub rose: 'Félicité et Perpétue' sported to produce 'White Pet' (or 'Little White Pet). The famous 'New Dawn' is a smaller, repeat-flowering version of its sport parent 'Dr. Van Fleet', a once-blooming Wichurana rambler. And 'New Dawn' has produced at least two sports of its own: a white-flowered version, and one with more double, quartered blooms, commonly called 'Awakening'.
Some varieties have produced numerous sports, and often these sports have produced sports of their own. The old Hybrid Tea 'Radiance' was the founding parent of a whole family of color and climbing sports, and even more prolific was 'Ophelia', another Hybrid Tea, which had about thirty sport descendants introduced into commerce.
Sports can revert, producing growth like that of the sport parent. Sometimes the growth takes over the whole plant; sometimes both forms continue to exist on the same plant.
Besides color and plant habit, sporting has produced the Moss roses, which sported from Centifolias and Damasks, and 'Chapeau de Napoleon', with its peculiarly mutated sepals. Sometimes a sport results in a different flower form: the very double 'Souvenir de la Malmaison' sported to 'Souvenir de St. Anne's', a semi-double form, as well as producing at least three other sports that were introduced into commerce. Not all sports are gardenworthy. I think a plant of the 'Dark Lady' that I had sported to produce some quite hideous short-petaled blooms; I didn't consider the possibility that it was a sport until I encountered the second monstrous flower.
I hope this helps.
Melissa
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Roses in landscape photos
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