The thorn-like protrusions on the stems of roses are actually called prickles. A thorn would be an entire stem or branch that has been modified to be hard and sharp. Prickles are extensions of the epidermis of the rose stem that has hardened. The difference is that thorns are entire stems, while the prickle is only part of the stem.
I guess every rose does NOT have its thorn. Bret Michaels may have been wrong botanically, but the song title “Every Rose Has Its Thorn” just sounds better than “Every Rose Has Its Prickle”.