Well stated, SlideRuleEra.
I would say that when using the ASD method, you determine the actual stresses using the known loads and geometry of the structure combined with section properties of the members. No factors are applied to the loads. Dead load is 100% of the dead load, concentrated live loads are 100% of the concentrated live loads, etc. Load cases are determined using combinations of dead, live, seismic, external pressure, wind, etc. In some cases the load case summations involve factors but they are not to be confused with LRFD factors. Stresses like axial and bending are combined using formulas.
Allowable stresses are then either found in tables or calculated based on material properties and section geometry.
A comparison of "actual" versus "allowable" for the various load cases completes the analysis.
I hope that did not muddy the waters too much!!