Yeah, it matters b/c of several factors. To understand the law on murder, you have to look at "motive." When new laws are enacted, like "hate crime" legislation, it is to fill a hole or gap that has been discovered. You can say, "murder is murder," but that doesn't cover that which is requisite to treat such crimes with equal due process -- it is too simplistic a view. "Hate crime" legislation came of age to ensure that the essential elements of malice were covered in prosecution -- IOW, there were some loopholes that needed filling. It wouldn't have been added unless there was a need, b/c to do so (to add it without need) would have made prosecution more difficult!
Every state's murder statutes go by different names, and certain elements vary. State and federal "hate crime" statutes and laws, respectively, close down these variances and is, therefore, a necessary tool.
Essentially, the elements of malice murder have traditionally been looked at as whether or not there was premeditation. Some defense lawyers were arguing that a hate-motivated murder didn't rise to that standard -- therefore, clearly malice killings were being argued down to second degree, or even voluntary manslaughter. What is most often known as second degree murder lacks premeditation -- and "passion of the moment" can be utilized for mitigation purposes in verdict and/or sentencing. It was a necessary move by our lawmakers to make certain that a lesser sentence didn't arise out of a good defense that sold mitigation within the bounds of technicality!