Currently there are Aspen, Willow, Western Juniper, Jeffry Pine, Western Red Cedar, Sugar Pine, White Fir, and Douglas Fir trees. Young variants exist as they grow up into mature trees.
The only gameplay difference between them at the moment is the amount of logs each provides when chopped up. Aspen and Willow provide very little wood as logs while Sugar Pine, White and Douglas Fir provide the most logs.
Eventually each type of wood may have different innate bonuses for crafting.