difference between "elect" and "appoint"

[Olmert]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #252 "American Government Questions Test (1)", question 7

The president has a number of responsibilities and one is to ......... ambassadors to foreign countries.

(a) elect
(b) appoint
(c) alert
(d) reject

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #252 "American Government Questions Test (1)", answer 7

The president has a number of responsibilities and one is to appoint ambassadors to foreign countries.

Correct answer: (b) appoint

Your answer was: incorrect
The president has a number of responsibilities and one is to elect ambassadors to foreign countries.
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what is the different between "elect" and "appoint"?

Olmert

[Linda]

Appoint: "To select or designate to fill an office or a position."
Elect: "To select by vote for an office or for membership."
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