I am reminded of the story of the Manhattan antique dealer who discovered he was in violation of a New York City law because he was operating without a secondhand seller license. "But, I'm an antiques dealer," he sputter with outrage when he was handed the $1000/day fine. Yes, but according to New York City regulations anyone selling items that are pre-owned is a secondhand dealer. It does bring to mind Barbra Streisand's song Secondhand Rose of Second Avenue. At one time the south end of Second Avenue in New York City was the location of a great many secondhand shops which sold anything from furniture to clothing as long as it had usable life. No doubt Second Avenue was zealously scouted by the uptown antiques dealers where the "finds" were relocated at a graduated price.
The point of the anecdote is that there is a legal component to the terms which may not have anything to do with value. For example, the term antique when it's applied to customs duty simply means that whatever it is that is being imported is 100 years old or older. The Staffordshire chamber pot filled with dried flowers in a shop window may be antique but it may have no more value than a pottery bowl from Walmart. Of course, if it came from the Wedgwood factory and has Enoch Wood stamped on the back, that's a different story. To knowledgeable dealers, the term antique is reserved for things made either before the Industrial Revolution (roughly before 1800) or during the early stages when objects still required trained crafts people to produce it. Objects made after 1830 and before 1900 are often designated as antique with no intention to deceive. Well designed objects made by notable manufactures of quality pieces are often listed as antique on hang tags. Other items may simply carry a price on the tag and since it's in an "antique shop" the assumption is that it is antique. The buyer should assume in such cases the item is old, pre-owned and probably vintage. A knowledgeable dealer should be able to tell you the age, the style (aesthetic period as an example), and anything else notable about it.
Vintage is a relatively new word applied to old, used items. The term acknowledges that an item is old and it borrows panache from the term as it is applied to wine. While you can be sure the item is old, you cannot assume that it is not currently being manufactured in the same form. Mid-twentieth century furniture by Harry Probber is vintage, valuable and sells for more than it did when it was new. Ralph Lauren vintage glassware in a pattern made a few years ago purchased used is secondhand and should sell for less than it did when it was purchased from Lauren.
The big caveat to buyers is that the terms applied to objects to designate age are in no way indicative of value. Design, craftsmanship, current taste, provenance and condition are all far more important than age.