I have been wondering about these two nouns for awhile.

Problem:
One of these nouns is less appropriate in more formal situations.

Explanation:
According to Dictionary.com, the noun “quote” has been accepted — at least informally — as a truncation of the noun “quotation” for more than a century.

However, most consider “quote” to be less formal than “quotation” and not appropriate in all situations.

For example, while many consider “quotes from the Three Stooges” to be acceptable, fewer consider “quotes from the Bible” to be acceptable.

I doubt that the phrase “price quote” will disappear from American English.

It’s valuable, though, to know that “quote” is a truncation of “quotation” and therefore is less formal.

Although using “quote” as a truncation of “quotation” does not lead to ambiguity (in contrast to “install” — a truncation of either “installer” or “installation”), I believe that this use is consistent with my “Devolution toward Simpler” linguistic hypothesis. It’s simpler to say the one-syllable word than it is to say the three-syllable word.

Solution:
Use “quote” in informal situations; use “quotation” otherwise.