A quote is an offer to do work at a price. An invoice is a request for payment for work that has been done or agreed.
One is a proposal that can be withdrawn or expire; the other is a financial document with tax consequences and a payment term attached.
A quote needs the scope, the price, what is excluded, and a validity date. Without the exclusions and the expiry it is an open-ended commitment.
An invoice needs a sequential number, the dates, both parties' details, the tax treatment and payment terms. Missing any of those is the commonest reason an invoice is queried rather than paid.
Generally it is an offer that becomes binding on acceptance, subject to its terms and expiry. Take your own advice on your jurisdiction.
Be explicit either way, and be consistent with how you will invoice. Mismatches cause most disputes.
On larger deals it is useful — it records acceptance before any payment is demanded.
Half an hour with your own data usually saves reading three of these. The guides will still be here afterwards.