RICK - I haven't compared part number by part number, but the only difference between a K161 & K181 was the crankshaft stroke. There were small & large bore K161's, 2-7/8" & 2-15/16" bore, and all K181's are 2-15/16". The K161's were all 2-1/2" stroke and all K181's were 2-3/4" stroke. I suspect they raised the wrist pin hole in the K181's pistons to accomidate the longer stroke, but Kohler may have changed the rod too, shortening the rod 1/8 inch would do the same thing. I've never actually compared the two parts from the two engines to see which Kohler did.
The valves, springs, keepers, carb, etc is ALL the same between the K161 & K181. The cam location is the same on both engines, so the same length valves are used in them both.