SPM and FreeSurfer are both morphometry tools. While SPM implements voxel-based morphometry, FreeSurfer represents surface-based morphometry. FreeSurfer enablea automatic compartmentalization of the brain into multiple anatomic regions and quantify tissue volume in these regions on an individual case basis, while SPM involves group-wise comparisons being a technique that objectively localizes focal changes of voxel values throughout the entire brain volume.
SPM and FreeSurfer are both morphometry tools. While SPM implements voxel-based morphometry, FreeSurfer represents surface-based morphometry. FreeSurfer enablea automatic compartmentalization of the brain into multiple anatomic regions and quantify tissue volume in these regions on an individual case basis, while SPM involves group-wise comparisons being a technique that objectively localizes focal changes of voxel values throughout the entire brain volume.
I believe that both SPM (Statistical Parametric Mapping) and FreeSurfer use a parametric approach (based on the normal distribution of the data). Both packages allow structural (VBM, cortical thickness/folding analysis, tractography using FS's Tracula) and functional (FS's FS-FAST) analysis.
There are tools in SPM or extension in SPM that allow you to do non parametric tests (SnPM) and some type of connectivity analysis for fMRI (dynamic causal modelling, psycho-physiological interactions). I am not sure if those are implemented or have their equivalent in Freesurfer.
There might be other differences (regressor orthogonalizations, cluster analysis, multiplie comparison correction,...) but I am not familiar enough with freesurfer to tell you more.