EDDIE51, it is entirely possible for brothers to have different blood groups.
When sex cells are produced (egg/sperm) the chromosomes arrange in what is known as "independent assortment." Basically, before a cell divides, they line up along the middle of the cell, and can line up any way they please.
When the resultant sex cells are formed, each will have a different chromosome (or indeed, a different PART of a chromosome) in it, and each chromosome will contain different genetic material.
Ultimately, this means that brothers could be very similar, or they could be a world apart. The chance of them being identical is very very very low.
With half brothers, they would share some of the same maternal/paternal DNA, but would have different DNA from the other parent.