Can someone help me understand some of the different options when performing a discriminant function analysis (I use SPSS in my research)?

I have traditionally computed prior probabilities from group sizes and selected to use a within-groups covariance matrix. As far as I understand it, using the separate groups covariance matrix calculates quadratic rather than linear discriminant functions...? Is this the same thing as a Fisher's Discriminant Analysis? If not, how do they differ?

In essence, I am trying to decide under what circumstances one would opt to use the separate-groups covariance rather than within-group - and if I should now go down this route.

My grouping variable includes 7 groups of with sample sizes between 18 and 68 or 6 groups with sample sizes between 40 and 68. My predictor variables (independents) consist of linear measurements of bones which have been logged.

Thanks you for any advice!