On --adjust:
If you use a significance cutoff of 5% then you'd expect 20 SNPs to be significant in your 400 SNP dataset just by chance (400*0.05=20). You can either use a new cutoff of 0.05/400=0.00125, OR you can use --adjust, which gives additionally to your original output files p-values adjusted with a variety of technologies like FDR or Bonferroni (see here). Either are fine to me.
On your question about different p-values:
As far as I know, PLINK can use several SNPs together in one logistic regression's model (have a look at slides 20/21 here. If you remove some of these SNPs, the entire model changes, so that the p-values of the other remaining SNPs change, too.
I'm slightly confused - are you running a logistic regression using --logistic or Fisher's exact test using --fisher?
(Also, are you using --adjust?)