They are similar in that they both come with the same benefits within the store such as financing options and rewards. They also both come with high APR’s. The main difference is the card branded with the MasterCard logo can be used anywhere MasterCard is accepted opposed to the standard Best Buy card which can only be used in the store.
You can’t choose which one you apply for. Your eligibility will be determined by your credit score. A better score gets the MasterCard and a person with a lower credit score will be given the standard store card. Also you could possibly be charged a $59 annual fee as well depending on your creditworthiness.