In obsolete|lang=en terms the difference between expel and dispatch
is that
expel is (obsolete) to fire (a bullet, arrow etc) while
dispatch is (obsolete) a dismissal.
As verbs the difference between expel and dispatch
is that
expel is to eject or erupt while
dispatch is to send a shipment with promptness.
As a noun dispatch is
a message sent quickly, as a shipment, a prompt settlement of a business, or an important official message sent by a diplomat, or military officer.