Perhaps I'm not the only one to have done a double take at Sotheby's loose language in their Instagram ad fed to me (and you?) today.
As Sotheby's should know perhaps as well as anyone, an auction estimate is not an appraisal. An auction estimate is a strategic figure designed to optimize results within a specific auction sale context.
An appraisal, by contrast, is an opinion of value (or, per USPAP, the act or process of developing such an opinion of value.). Depending on the type of value being appraised and the effective date of valuation used in an appraisal, and also depending on the specific auction sale context for a given estimate, an appraisal and an auction estimate for the same item may be similar -- or in many cases, they will differ significantly.
Sotheby's auction estimate for a work may be far higher than the estimate that a small auction house in the Midwest might give for the same work -- and both might be informed, accurate reflections of how best to market that item within their respective sale. These are not appraisals but rather context-bound marketing figures that reflect auction house perceptions of a specific market.