I think there is differences in the 'tusk' teeth due to their continuing growth process, which is not seen in 'permanent' teeth. I'm guessing the root end of the 'tooth' would have the dentine, nerves, pulp and enamel like or own teeth.
Aha!, I was correct:
The visible, ivory part of the elephant's tusk is made of dentine with an outer layer of enamel. Elephant ivory is unique which when viewed in cross-sections reveals criss-cross lines that form a series of diamond shapes (Schreger lines- see below). Elephants tusks never stop growing so some old bulls display enormous examples.
One mammal that only grows only one toothy canine tusk is the Narwhal. It's ivory rapier can grow up to 9 feet (2.74 metres) long. It's spiralling tusk was frequently sold as a unicorn's horn in ancient times, thought to have magical powers. Didn't help the poor narwhal it came from in the end tho. They use them as clubs rather than spears, striking fish to stun them before eating them. They apparently are somewhat porous and the dentine has nerve endings which enable them to detect among other things, water salinity, Female pheromones, etc. males have a ritual get together where they clash their tusks together en-mass, but do not fight with them. Guess they are comparing the length of their toothy member rather like we compare other bits of our more visible anatomy (heir's is hidden in a sheath to cut down on water resistance