Model will take you to the Fit Model platform where you can perform a standard least squares analysis based on the main effects from your design. Screening uses a different calculation, based on the symmetry of the design. For a 2-level design the results will be identical.
The inclusion of centre points will result in the least square estimates differing slightly from the contrast estimates in the Screening platform. Also, the centre points will contribute to the pure error term in the Fit Model ANOVA allowing you to assess lack of fit. Assessment of fit is not part of the Screening platform, because building a predictive model it is not the primary purpose of a screening DOE.
This video attempts to explain the contrast calculation in the screening platform, and its equivalence to the fit model results