One is simply a shortened version of the other - turning a sentence into a phrase. This is quite common in casual English. As long as the meaning of the shortened version is understood by the reader, it is fine.
In this specific case, I assume the email reader and writer both know something is being purchased, both know it will be delivered, and both know it will be paid for with a cheque. The only issue is when the cheque will be sent. So a short phrase is fine.