Alzheimer’s disease (AD) and its precursor stages present an inherent ordinal structure, progressing from cognitively normal (NOR) through mild cognitive impairment (MCI) to full AD. This work exploits that natural ordering by comparing nominal and ordinal classification approaches applied to structural MRI (sMRI) data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). We evaluate a linear Support Vector Machine (SVM), a Logistic Regression (LR) classifier, as well as LogAT and LogIT as nominal baselines, and the Support Vector Ordinal Regression EXtension (SVOREX) as an ordinal counterpart. All classifiers operate directly on voxel-level gray matter (GM) maps and are evaluated across binary (six pairwise combinations), three-class and four-class settings using Correct Classification Rate (CCR), Mean Absolute Error (MAE) and Average Mean Absolute Error (AMAE) under a 5-fold cross-validation protocol. Results show that SVOREX consistently achieves the lowest ordinal errors, particularly in the clinically most relevant multi-class scenarios, supporting the value of incorporating class-order information in Alzheimer staging from MRI data.