Yes it is but cane is short for primocane.
Jessica M. Cortell has written: 'Effect of floricane number on primocane growth, yield components, and cold hardiness in 'Marion' trailing blackberry' -- subject(s): Blackberries, Yields, Hardiness, Pruning, Effect of cold on
No, blackberry bushes do not have annual rings like trees do. Annual rings form in trees due to their woody stems, but blackberry bushes have flexible, non-woody stems that do not produce these rings.