That's going to depend on where the data is located relative to the defining values of the two coordinate systems. WyLam is a statewide coordinate reference system (CRS) that uses the Lambert conformal conic map projection. The Wyoming State Plane zones use the transverse Mercator map projection. Both are conformal so they maintain shapes (angles) rather than distances or areas.
If the area of interest happens to fall near a central meridian or standard parallel, etc. of one of the CRS, that will minimize the distortions due to the projection. It could also matter if different geographic CRS were used.
Note: Depending on the software / tool that you used, the buffer may have been built using geodesic distance calculations and the results then projected into the data's CRS.
For the undistorted areas, only the central meridian and standard parallels matter in a conic projection, and only the central meridian and scale factor do in transverse Mercator.
Central Meridian = -107.5
Standard Parallel_1 = 41.0
Standard Parallel_2 = 45.0
False Easting = 500000.0
False Northing = 200000.0
Latitude Of Origin = 41.0
**Wyoming East (NAD 1983)**
Central Meridian = -105.1666666666667
Scale Factor = 0.9999375
False Easting = 200000.0
False Northing = 0.0
Latitude Of Origin = 40.5
In the State Plane zone, at 42N, 104d 18' 30"W, scale is 0.9999997, for example.