The Let's Pretend rainbow logo is on the side of the weapon.
The actual blade geometry isn't rotating, it's a scrolling UV shader that fakes the look of a rotating blade.
It is the most expensive melee weapon, with the cost of $100,000, and one of the most expensive weapons overall.
Like the Chainsaw, it has unique attacks which can be used with the Secondary Fire button.
When used on an enemy on the ground, an animation plays where Playa jabs the chainsaw into the body and grinds away; if the weapon is switched during this animation, it continues with whatever weapon is selected. This attack is capable of instantly killing Brutes, Zombie Gat, and Professor Genki.
When selecting the Woodsman, even for the slightest moment, Playa is locked into doing a significantly lengthy animation of pulling its cord to start it up, and cannot change weapons while doing so.