TukeyHSD function or glht for post-hoc test after ANCOVA

Question

I'm currently performing an ANCOVA in R testing the difference in the levels of fungi depending on the types of fungi while correcting for a difference in the age of the fungi (days).

model <- aov(fungi_level ~ fungi_types + days, data = fungi_data)
Anova(model, type = "III")

Here, I find a significant difference between the different fungi types and want to perform post-hoc testing. As far as I can see there are (at least) two different ways to perform TukeyHSD:

TukeyHSD(model, which = 'fungi_types')

Which gives an error: "... non-factors ignored: days"

or

PostHoc <- glht(model, linfct = mcp(fungi_types = "Tukey"))

Does anyone know the difference between the two different tests? It seems that the glht is more restrictive when looking at the p-values.

Thanks a lot!