A quote is a proposal. It is often printed on the same letterhead as the contract, with a list of items, a term, and a total. That list can look like a promise, but the contract it refers to is usually the document that controls what happens when you make a claim.
Read what the quote is tied to
Look for a reference to a contract form number, a plan name, or a version date. If the quote points to a form you have not seen, request that form before you accept the quote. A quote that cannot be matched to a contract form is not yet a complete record of what you would buy.
Compare the item lists line by line
Check that the items in the quote match the items in the contract. Where the quote lists an item the contract never names, or the contract names an item the quote omits, ask which document the seller will stand behind. Then read the exclusion section of the contract, because an item listed in the quote can still be limited there.
Note what a quote cannot do
A quote does not replace the signed agreement, and it does not show the cancellation terms, the waiting period, or the transfer rules unless those are restated in the contract itself. Keep the quote with the signed contract, and do not treat the quote as the policy.