The main difference between Chief and Cheif is that the Chief is a a leader or ruler of a people or clan and Cheif has no English definition. It is generally be misspelled.
Cheif
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Chief (noun)
A leader or head of a group of people, organisation, etc. from 13th c.
"All firefighters report to the fire chief."
Chief (noun)
The top part of a shield or escutcheon. from 15th c.
Chief (noun)
An informal address to an equal.
"Hey, chief."
Chief (adjective)
Primary; principal.
"Negligence was the chief cause of the disaster."
Chief (verb)
To smoke cannabis.
Cheif (noun)
Obsolete spelling of chief.
Chief (noun)
a leader or ruler of a people or clan
"Chief Banawi"
"the chief of the village"
Chief (noun)
the head of an organization
"a union chief"
"the chief of police"
Chief (noun)
an informal form of address to a man, especially one of superior rank or status
"it's quite simple, chief"
Chief (noun)
an ordinary consisting of a broad horizontal band across the top of the shield.
Chief (noun)
the upper third of the field.
Chief (adjective)
most important
"chief among her concerns is working alone at night"
"the chief reason for the spending cuts"
Chief (adjective)
having or denoting the highest rank
"the chief economist of a leading bank"
Chief (noun)
The head or leader of any body of men; a commander, as of an army; a head man, as of a tribe, clan, or family; a person in authority who directs the work of others; the principal actor or agent.
Chief (noun)
The principal part; the most valuable portion.
Chief (noun)
The upper third part of the field. It is supposed to be composed of the dexter, sinister, and middle chiefs.
Chief (adjective)
Highest in office or rank; principal; head.
Chief (adjective)
Principal or most eminent in any quality or action; most distinguished; having most influence; taking the lead; most important; as, the chief topic of conversation; the chief interest of man.
Chief (adjective)
Very intimate, near, or close.
Chief (noun)
a person who is in charge;
"the head of the whole operation"
Chief (noun)
a person who exercises control over workers;
"if you want to leave early you have to ask the foreman"
Chief (adjective)
most important element;
"the chief aim of living"
"the main doors were of solid glass"
"the principal rivers of America"
"the principal example"
"policemen were primary targets"