field vs domain

field and domain both are nouns.

Word	Noun	Adjective	Verb	Adverb
field	Yes	No	Yes	No
domain	Yes	No	No	No

As nouns, domain is a hypernym of field; that is, domain is a word with a broader meaning than field:

Other hypernyms of field include knowledge base, knowledge domain.

As nouns, field and domain are synonyms defined as:

Other synonyms of field include area, arena, orbit, sphere.

field (noun)	domain (noun)
a particular kind of commercial enterprise	the content of a particular field of knowledge
a place where planes take off and land	people in general; especially a distinctive group of people with some shared interest
a branch of knowledge	(mathematics) the set of values of the independent variable for which a function is defined
the area that is visible (as through an optical instrument)	territory over which rule or control is exercised
(mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1	a particular environment or walk of life
all of the horses in a particular horse race
all the competitors in a particular contest or sporting event
(computer science) a set of one or more adjacent characters comprising a unit of information
a piece of land cleared of trees and usually enclosed
somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected
a piece of land prepared for playing a game
a region in which active military operations are in progress
a region where a battle is being (or has been) fought
a geographic region (land or sea) under which something valuable is found
extensive tract of level open land
the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it
a particular environment or walk of life

field (verb)	domain (verb)
select (a team or individual player) for a game
answer adequately or successfully
play as a fielder
catch or pick up (balls) in baseball or cricket