Put another way, Base and Bonus miles go into your Skymiles account. These are the miles you can use to book awards. When you look at your Skymiles balance, it will be the sum of Base and Bonus miles earned minus miles expended.
MQMs are simply a counter for elite status. They cannot be redeemed for anything, but once you cross the MQM threshold for a certain medallion level, you will see that your account is upgraded to that level within a few days.