If a tax exemption applies to everyone in a given tax jurisdiction — such as in the groceries example above — sellers do not need to collect an exemption certificate for those particular sales. However, when an exemption is more narrow, a buyer must provide an exemption certificate in order to prove to the seller that tax should not be charged.
Entity-based certificates are for organizations that are exempt because of their standing as a government agency, nonprofit, or some other qualifying status. These certificates allow organizations to purchase items without paying tax, regardless of how they’ll be used.
Usage-based certificates allow for the purchase of items only if they’re to be used for a qualifying purpose — for example, if they’ll be resold. An organization with an exemption for resellers (often called a “reseller permit” or “resale certificate”) can only avoid paying sales tax on items it will resell; it would have to pay sales tax on products the organization would use for other purposes, such as office supplies.
Individuals from non-sales-tax states who purchase items in a state that does charge sales tax typically need to prove their residency to avoid paying tax. (That is, if the state in question allows this. Washington is one state that does; however, the state leaves it up to the seller whether to charge tax, and there are a host of qualifying factors.)