Why library sizes in the DGE object are different from original library sizes? And which library sizes should be used in differential expression analysis?

dge <- DGEList(counts = Counts,
               group = sampleInfo$Group,
               genes = genes[which(rownames(genes) %in% rownames(Counts)),]
)

It appears you have filtered your genes, and probably set keep.lib.size = FALSE when doing so.

Example data from ?glmQLFit

>  nlibs <- 4
>  ngenes <- 1000
>  dispersion.true <- 1/rchisq(ngenes, df=10)
>  design <- model.matrix(~factor(c(1,1,2,2)))

     # Generate count data
> y <- rnbinom(ngenes*nlibs,mu=20,size=1/dispersion.true)
>  y <- matrix(y,ngenes,nlibs)
>  d <- DGEList(y)
>  d <- normLibSizes(d)


> colSums(y)
[1] 20298 20327 19928 20307
> d$samples
        group lib.size norm.factors
Sample1     1    20298    0.9941360
Sample2     1    20327    1.0029198
Sample3     1    19928    1.0044059
Sample4     1    20307    0.9985705

## fake filter
> keep <- sample(1:1000, 900)
> d.filt <- d[keep,, keep.lib.sizes = FALSE]
> d.filt$samples
        group lib.size norm.factors
Sample1     1    18223    0.9941360
Sample2     1    18298    1.0029198
Sample3     1    17862    1.0044059
Sample4     1    18175    0.9985705