A possible problem is that the runway surface description and estimated braking action are being intermixed.
Dry describes the runway surface, as would wet or contaminated (with sub descriptions).
Good is the estimated braking action for the description and is relative to the description; i.e. wet – good implies ‘good’ braking action for wet conditions, similarly dry snow – good, is ‘good’ for snow contamination, but is not the same as wet. The combination of dry – good is usually self-evident as it represents the best condition.
The background for this is in ICAO Annex 14 Chapt 6, Att A.
“If the surface is affected by snow or ice and the braking action is reported as “good”, pilots should not expect to find conditions as good as on a clean dry runway (where the available friction may well be greater than that needed in any case). The value “good” is a comparative value and is intended to mean that aeroplanes should not experience directional control or braking difficulties, especially when landing”.
The choice of which parameter to use when determining the takeoff data may depend on the basis of the aircraft’s certificated data.
Thus any confusion in the takeoff calculation might arise from the performance computer, which presumably for the dispatch case, should be based on AFM; thus check which terms the AFM uses for determining takeoff performance.
Note that ‘slippery’ is a generic term (Boeing) covering wet, and snow and ice descriptions, which may add to the confusion.
For landing distance (advisory), Airbus tends to use a descriptor with type and depth of contamination, whereas Boeing (QRH) use the estimated braking action either from the tower or with greater variability from pilot reports.