I'm inclined to agree with cnas122. Familiarity will come with time, so long as you take the time to really look these materials over when you get the opportunity.
As for my 2 cents' worth, I've noticed most bone-handled knives usually take & have a higher polish, and even more so with time (Case duplicates the effect with their 'Pocket Worn' bone series, which are finished to a smoother, shinier effect). With polished bone, I've also noticed a certain 'depth' to the finish, almost looks liquid (like a deep, highly polished finish on a car). When tested with a fingernail, bone is usually quite hard. The fingernail will usually just skate across it, without 'biting' or leaving any mark behind. If you inspect the ends of the scales, or the inside surfaces of the jigging marks, bone will have a lot of 'pores' in it (use a magnifier, and very bright light). Some jigged wood handles look like they could be bone, but won't be as hard or scratch-resistant under a fingernail. If inspected under magnification, wood will show it's grain, which won't be seen with otherwise similarly finished bone. Synthetic handles that are made to look like bone or stag won't show any pores or (real) grain at all. That's a dead giveaway. Plastic always looks like plastic, close up.
With stag, I haven't seen too many examples as shiny as bone. Most of the smooth antler handles I've seen have a somewhat greyish or 'salt & pepper' look to them, whereas smooth, undyed bone will usually look whiter, kind of milky. Also, with the black, rougher finish usually seen in the recesses of 'gnarly' stag handles, the black stuff is often somewhat flaky in nature. Sometimes it'll peel off, if you get a fingernail or toothpick under it. Some bone handles are carved (jigged) to resemble stag ('bone stag', or 'stag bone'), but the man-made carving/jigging usually can't hide from close inspection. Most stag doesn't feel quite as hard or slick to me, compared to bone, when tested with a fingernail.
The very few ivory handles I've actually looked closely at, have a somewhat 'creamy' or 'buttery' appearance to them, with some 'depth' in the finish (similar to bone), especially when polished.