Hi Rob,
David has shown a cross-sectional cut through ivory, which displays the Schreger's Line criss-crossing the cut surface. Other lines are also visible as fine concentric rings (around a small central pulp area that is not shown in that picture).
Tusks are modified teeth, and all tusks have some element of the central pulp found in teeth. What we recognize as ivory is the equivalent of tooth dentine that makes up the majority of the ivory tusk.
The straight lines on your ivory figure are caused by longitudinal sections through these concentric rings. This is definitely ivory and not bone.
A nice description of ivory, bone, horn, and antler, and their care, can be found on this site:
https://www.canada.ca/en/conservatio...rn-antler.html