KINGDOM: Fungi
DIVISION: Ascomycota
CLASS: Sordariomycetes
ORDER: Xylariales
FAMILIES: several
Here "xylariacous" refers to members of the fungus order Xylariales, which doesn't have a good English name. Sometimes its species are referred to as "wood decayers," but members of other fungus groups also decay wood.
The black-and-white little fungus at the left (only 0.4 inch or 10 mm high) is a member of the genus Xylaria, growing on the wood of a log fallen in the woods.
At the right, that's Candlesnuff, the name from back when everyone snuffed candles instead of flipping off the lights. It's Xylaria hypoxylon, also on a dead log
At the left is another xylariacous wood decayer family, a good guess being that it's a member of the genus Hypoxylon. It's growing as a crust on the decaying bark of a dead twig. If you look at the crust very closely with a hand lens, you'll see tiny (less than 1/32-inch, 0.8 mm), black, slightly raised dots. These dots are small cavities called perithecia (sing., perithecium), which are round or flask-shaped bruiting bodies with a pore through which ascospore-type spores can be discharged into the air. These ascospores then germinate to form new fungus bodies.
All members of the Xylariaceae should be considered inedible.