The difference between a continuous factor and discrete numeric factor has to do with the way in which you want to treat the effects from each from a modeling perspective. Discrete numeric factors have an implicit assumption from a modeling point of view that there is no factor space available between the values and there is an implied order for the levels. Continuous factors have a modeling implication that there is a continuum of values the factor may have wrt to the response between the levels. See the JMP online documentation here for more details:
Not sure I agree with @P_Bartell on this. My understanding is that a discrete numeric variable is modelled as continuous. Conceptually the variable is continuous but for purposes of design generation we want to impose constraints on the possible values that will appear in the design.
@David_BurnhamYes, I did word my initial response rather poorly didn't I? I was thinking more from a conceptual point of view especially when estimating polynomial effects in that choosing a continuous factor will allow for more flexibility wrt to the levels that JMP Custom Design algorithm will find for a specific model, number of runs, etc. As the documentation suggests, all the levels for a discrete numeric factor may not appear in the design. Hence, if the person wants to insure that all desired levels of the discrete numeric factor are included in the design, then using the Screening Design platform might be a better choice. Lots to consider.