How to distinct them?

Do you mean "district"?

The correct wording for your thread title should be "How to distinguish...."

distinct?? did you mean district?

I have bolded the entries most people would associate with these words

http://dictionary.reference.com/search?q=domain
do·main noun.
1. A territory over which rule or control is exercised.
2. A sphere of activity, concern, or function; a field of expertise
3. Physics. Any of numerous contiguous regions in a ferromagnetic material in which the direction of spontaneous magnetization is uniform and different from that in neighboring regions.
4. Law.
1. The land of one with paramount title and absolute ownership.
2. Public domain.
5. Mathematics.
1. The set of all possible values of an independent variable of a function.
2. An open connected set that contains at least one point.
6. Computer Science. A group of networked computers that share a common communications address.

realm. noun

1. A community or territory over which a sovereign rules; a kingdom.
2. A field, sphere, or province: the realm of science. See Synonyms at field.

realm is more usually applied where a sovereign or king is involved as opposed to a lesser type of royal such as Lord or Duke

dis·trict (dstrkt) n.

1. A division of an area, as for administrative purposes. (usually a smaller area of land than associated with territory)
2. A region or locality marked by a distinguishing feature: went to the lake district for their vacation.


ter·ri·to·ry Audio pronunciation of "territory" ( P ) Pronunciation Key (tr-tôr, -tr)
n. pl. ter·ri·to·ries

1. An area of land; a region.
2. The land and waters under the jurisdiction of a government.
3.
1. A political subdivision of a country.
2. A geographic region, such as a colonial possession, that is dependent on an external government: the territories of the Holy Roman Empire.
4. often Territory
1. A subdivision of the United States that is not a state and is administered by an appointed or elected governor and elected legislature.
2. A similarly organized political subdivision of Canada or Australia.
5. An area for which a person is responsible as a representative or agent: a salesperson's territory.
6. Sports. The area of a field defended by a specified team: punted the ball deep into the opponent's territory.
7. Biology. An area occupied by a single animal, mating pair, or group and often vigorously defended against intruders, especially those of the same species.
8. A sphere of action or interest; a province. See Synonyms at field.

All these definitions forterritory would be usual and depend on the context (what you are talking about)

NB my emphasis and interpretation is bold or italics
DP

Reply for my mistake.
Sorry ,I have made a mistake in my last topic.Thank you for telling me!It's district, not distinct.
Thank you again!

It is a pleasure to help you nancycumt. Perhaps you would like to practice your english by posting on another thread or topic. Many people here would like to know more of china and its fabulous culture.