The terms Billable and Non-Billable expenses are normally associated with say a consultancy company where they bill consultants out to their clients. Therefore Billable expenses will be paid by the client whereas Non-billable will be paid by your employer. What's included in both is subject to the contract your company has with their client.
There is no specific abbreviation for the term WIRE because when the payment is being made using this option, you will not see the physical movement of funds. It is all electronic. It is just like a current passes through Wire.
Therefore Electronic movement of funds is campared with WIRE.