On Billing Grid,

Start Date - is the date on which billing starts for the child. Start Date of the Billing Grid entry comes from the child's schedule start date.

End Date - is the date on which the billing stops. End Date on Billing Grid comes from the End Date of child's schedule. 

There is one more important date on Billing Grid,

Next Billing Date (NBD) - is the date when upcoming charges for the bills will post.

NOTE: By Default, when a new bill is created, Start Date is equal to the Next Billing Date. Until the bill is charges, you can edit the Start Date, Next Billing Date and Amount of the bill. However, once a bill is charged, you cannot edit the Start Date, NBD, and Amount of the bill.