The billings report will simply report on the number of payments that come in the door from any invoice successfully processed (or money out the door from refunds).
MRR works like this: Every day, we look to see the recurring charges that are active (i.e subscription is in its billing cycle). We sum up all of those charges so you can see, at any point in time, the amount of monthly revenue you can predict. For charges that are longer than a month (i.e. yearly plans, we normalize those to 1 month aka divide by 12).
The monthly view of MRR is simply the MRR on the last day of the month.
- An invoice for a subscription worth $100 paid on Jan 15 will show as + $100 in the Billings
- That $100 charge on the invoice will have a start and end date (i.e. Jan 15- Feb 15). This time range represents the monthly billing cycle. So, this subscription will contribute $100 to MRR. On any day in that time range (Jan 15-Feb 15) you could look at MRR and see this subscription contributing $100 in MRR.
A good article to help clarify: https://blog.profitwell.com/understanding-saas-accounting-saas-bookings-saas-revenue-saas-collections