What differentiates the entry procedures for spins and snap rolls?
A snap roll isn't a roll.  It's an &quot;enhanced&quot; spin, done horizontally.
A normal spin entered from level flight at 1G stall speed has an initial roll component along with the yaw component as the wing drops at the stall.
The same thing happens in a snap roll, except that the spin is entered with an accelerated stall, well above level flight stall speed and with power, with both the roll and yaw initiation enhanced with aggressive rudder and aileron input to get the horizontal auto-rotation roll-yaw going as fast as possible.
Because the snap is done in an accelerated stall, the stall can be broken immediately with forward stick, and aggressive opposite control inputs have to be used to overcome inertia to stop the snap roll.  You initiate the left snap with the hard stick back/left and left rudder, and recover with hard stick forward/right and right rudder when about 3/4s of the way around.
You don't actually need aileron; airplane can snap roll quite nicely with no aileron, just rudder, it'll just be a bit slower.  A pilot can enter a snap roll accidently just from mishandling, say pulling too hard in a turn and inducing an accelerated stall with the ball off center, and if the airplane has a sharp stall break, around you go, and before you've figured out what happened you're already right side up again.
If you hold the control inputs and keep the snap-roll going, you eventually arc down until you're snap-rolling vertically, or spinning the old fashioned way.