From front to back: (off screen, itty bitty American Beech), Red Oak, Cucumber Magnolia, (really, really, itty, bitty white oak) Tulip Tree. Spacing is around 30-45 feet between trees, the beech is closer to the oak than any of the others, because the oak is elderly.
Acair Fearann 
Does American beech have that smooth grey bark that copper and other beeches seem to?
It does, almost the same as the European beech. Its a bit hard to tell the standard (green) European beech and the American beech apart. Except, unlike the European beech (both regular and copper) the American is usually not used as a lawn tree, being rather slow to establish and disliking fertilizer, soil disturbance, and transplanting.
Young American beeches generally keep some or all of their leaves through the winter, a dried, pale gold. Very distinctive in the forest!