Answer: If one branch or cane on a rose bush is very different (leaf texture or color, amount of thorns, type of bloom, etc.) from all the others and perhaps does not flower, it is usually a cane sent up by the root stock of a grafted rose. If you look carefully around the base of your plant (maybe even under the surface a bit), you should find the graft union; if this a shoot from below the union, cut it off as short as you can.
Actually, roses do go to seed (rose hips are the seed pods) but regular deadheading will prevent that if desired. A cane as you described would not be the cause or result of the rose setting seed.
Good luck with your rose!
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