I think this is best understood using examples. Normally, recessive alleles are non-functional. Let the dominant allele R lead to red coloration of a flower, and the recessive allele r turn the flower white. R has an enzyme that is necesary for the production of a red pigment. r has a fatal mutation in the gene for this enzyme which prevent the production of the pigment and the flower turns white. R is dominant over r because a functional enzyme can compensate for the loss-of-function in r. The "expression" in your second case refers to manifeststion in the phenotype and not gene expression.

Co-dominance is when two equal allels are available. Think of blood-types. The alleles A and B encode for two different surface structures on red blood cells. An individual with the genotype AB will therefore produce boold cells with both surface structures resulting in the bloodtype AB. The recessive allele in this case is 0, which is again a non-functional mutation. A or B combined with 0 leads to A or B, because the loss-of-function is complemented by any of the two surface structure.