After sight refers to a period calculated from the date a bill of exchange is presented to and accepted by the drawee, not from the date written on the bill.

Simple Meaning:

The payment period starts when the bill is seen and accepted by the person who has to pay.

Example:

If a bill is payable 60 days after sight and it is accepted on 10th March, the due date will be calculated from 10th March.

Difference:

After Date → Time counted from the date on the bill

After Sight → Time counted from the date of acceptance

In short, “after sight” means the credit period begins from the date the bill is accepted.