Despatch, n. & v.
Same as Dispatch.
Shades of meaning
Fernald has no entry of its own for despatch; he lists it under kill, quicken, send.
Where he writes about it:
To despatch is to kill swiftly and in general quietly, always with intention, with or without right. — from kill
To despatch is to do and be done with, to get a thing off one's hands. — from quicken
To despatch an enemy is to kill him outright and quickly; to despatch a messenger is to send him in haste; to despatch a business is to bring it quickly to an end. — from quicken
Despatch is commonly used of single items. — from quicken
A good general will improve roads to facilitate the movements of troops, hasten supplies and perfect discipline to promote the general efficiency of the force, despatch details of business, expedite all preparations, in order to accelerate the advance and victory of his army. — from quicken
To despatch is to send hastily or very promptly, ordinarily with a destination in view; to dismiss is to send away from oneself without reference to a destination; as, to dismiss a clerk, an application, or an annoying subject. — from send