Copied from Darvin’s comment on Observation 4530:

“In California, both Armillaria mellea and A. ostoyae have a thick, felty annulus and they are the only Armillaria species here to have that character. They differ by the color of both the cap and the annulus.
A. mellea has a white to yellow edge on the annulus, the cap is honey yellow and the disc is darker than the margin giving it a two-tone appearance. The cap is smooth and the hairs are indistinct.
A. ostoyae has a brown edge on the annulus, the cap is brown with dark hairs.”

Another quick rule is that A. mellea tends to grow on hardwoods and A. ostoyae on conifers. Tom Volk definitely id’ed a collection from southern California growing on hardwood as a slightly unusual form of A. mellea. I also sent him a sample from Santa Cruz that came out as A. mellea. Apparently the California material mated with the true A. mellea, but it was not a typical mating. Macroscopically I remember Tom noting that the California material has a scalier cap than classic A. mellea (which is smooth). Based on his key it looks like microscopy and and in particular looking for clamps at the base of the basidia is the only way to be sure. Personally I have a hard enough time find a good basidia, much less figuring out whether there’s a clamp at the base.