Here's a direct comparison of natural amber vs. high impact polystyrene (HIPS) "lemon amber". Note that HIPS beads can show surface wear, dirt and pitting that makes them look very "natural". In this case the color is a dead give-away. I haven't seen any HIPS beads (yet) that were colored to look more like natural amber, but I suppose they are out there.
Another property that can be confusing is that HIPS is a fairly low density plastic so it may "feel" like real amber. Amber has a density of around 1.05 - 1.10 g/cc, and HIPS, 1.03 - 1.06. The HIPS beads will therefore "pass" the salt water float test used to confirm real amber.
By contrast, other plastics used to imitate amber are higher in density, will "feel heavier" and also sink in the salt water test.
Generic phenolic resins, e.g.Bakelite: 1.36 g/cc
Galalith (casein): 1.35
acrylic: 1.17 - 1.20
Note that the density of plastics can vary a bit, due to the very wide variation in formulations that may included additives, dyes, etc., so these values are all approximate. Theoretically, you might, for example, find an acrylic bead that is low enough in density that it will pass the salt water float test.