As far as I can tell "Star" is a commercial name for a BL21 derivative. If the Star strain has a mutation that is not found in the original BL21 strain then they are obviously different. If you care about the exact genome sequence of the strain, you should try to obtain it from the vendor of the strain. Note that the DE3 designation indicates the presence of the λDE3 prophage that expresses the T7 RNA polymerase and is not present in all the BL21 strains that people use.