Case's product pages give a bone handle a Handle Finish of Smooth or Jigged, and Case's handle key puts both under one code, 6. The names are Case's own: Peach Seed is a jig Case calls a signature of the brand, BoneStag is "genuine bone" jigged and hand-flamed to look and feel like stag, and Pocket Worn is a hand-finish for a carried-for-years feel.
Case records the finish apart from the material. Its product pages carry a "Handle Finish" line reading "Smooth" for its Natural Bone and Chestnut Bone handles and "Jigged" for its Amber Bone.
Case's handle key gives one code, 6, to "Smooth/Jigged Bone (Various Colors), Jigged Synthetic (Various Colors), or Jigged Laminated Hardwood," so in Case's usage jigged names a finish that synthetic and laminated hardwood handles can carry too. Reading the rest of a stamped number is the job of how to read a Case pattern number; jigging in general belongs to the jigged bone entry, and bone as a material to the bone handle entry.
Peach Seed, BoneStag and Pocket Worn appear in the product data for Case knives on this site; Gator, Platts and Second Cut are names from Case's own pages.
No Case page cited here says how a jig is cut: even Second Cut is jigged "to look like" hand cutting. The "Handle Material" line, not the jig name, says what a handle is made of, and the bone and stag care answer covers the upkeep. For what a name meant on an older knife, the source is Case itself.