There is a difference. This choice, ordinal vs nominal, should be driven by what your response variable represents.
If you have a sufficiently recent version of the Statistics Toolbox, use the fitcecoc function for ordinal labels. Set 'Coding' to 'ordinal' and 'Learners' to 'Discriminant'. For categorical (nominal) labels, simply use fitcdiscr; class labels are treated as nominal by default.