hi,
Ideally they should not differ. And yes, snapping distances are not added (as far as I am sure). Do you have problems with all the pairs ? If not, just have another look at your cutoff distance parameter in your settings for OD matrix. This should not be the reason, but just have a look.
As the documentation suggests, OD matrix is a quick solver and does not take into account shapes. May be there are slight differences in the manual version and OD (batch) versions of the algorithms. I stand under correction.
Probably you should quantify your differences. Are they always differ by same amount, same percentage, may be some peculiar network edge common to all your (error) paths.