I doubt that is Illicium. Buds are all wrong. Illiciums buds are pointed and reddish. (I just checked mine). Floridanum has distinctive odor/fragrance when leaves are bruised. I love the smell.

And it doesn't look like Red Bay buds either. Red bay leaves are distinctive in odor/taste as well.

I wonder if yours is Symplocos tinctoria (Common Sweetleaf/Horsesugar). Is this evergreen? Leaves should have a sweet taste. Spring blooms are small/white in clusters.

Yeah I was looking more at the leaf shape than the buds. I'll go back and check to see if they have an odor or taste.

That leaf shape is sort of common to a LOT of plants. Did you mention if you know this was evergreen?

Not sure if it's evergreen, but I suspect it probably is. It's growing behind the fence around an old cemetary that backs up to a small creek.

Note that the leaf margins are actually not completely smooth in the upper half. This could be diagnostically significant.

General aspect resembles something along the Family lines of oaks or chestnuts.

But oak buds are also pointed. These whitish rounded buds look like next spring's flowers to me. Here is a better shot of a leaf I found on the web (of Symplocos). Not saying it is Symplocos for sure, but sure looks like it to me.

No doubt it's Symplocos tinctoria, I see it occasionally in the mountains between 2000'-3000' in poor dry soils and often along side Kalmia latifolia.

Yes these all look similar. Seems unexpected that the Kalmia would be in dry soils.