"Galleon" is one of those quasi-nautical terms that get tossed around by people who know what they're talking about and, more often, by people who don't.
When I run into questions like this I generally go to the relevant volume of the Conway's History of the Ship series. So far as I know, those books are the most up-to-date pieces of genuine scholarship about the subject. Here's the definition from the relevant volume, titled Cogs, Caravels, and Galleons: The Sailing Ship, 1000-1600:
"galleon. Sea-going full rigged ship of the sixteenth century or later, characterised by a relatively high length-to-breadth ratio, a long beak under the bowsprit and a crescent profile rising somewhat higher at the stern than at the forecastle. Compared with carracks, the lines of the galleon were finer, the superstructures lower, and under sail both speed and handling were superior. Galleons were usually heavily armed, although they were not necessarily specialist warships. The term came to be loosely associated with the Iberian powers, and in particular Spain, so that by the seventeenth century almost any large Spanish ship could be described as a galleon."
I'd add that the term was sloppily used even later than that. When Commodore Anson sailed on his famous round-the-world voyage in 1737, part of his mission was to capture the "Manila galleon."
I think most serious maritime historians nowadays use the term mainly to describe large warships of the sixteenth and very early seventeenth centuries. The San Martin, flagship of the Spanish Armada, certainly was a galleon. So were the big ships of the English fleet in 1588, like the Ark Royal and the Revenge. The Golden Hind was too small to be called a galleon, and the Mayflower and Susan Constant weren't. (They were merchantmen.) Caveat: I think most maritime historians would agree with those distinctions, but maybe not.
"Galleon" is a useful term under some circumstances. Another one that's used even more casually is utterly useless: "tall ship." That one's one of my pet peeves. OK, the great poet John Masefield used it once in his poem "Sea Fever." ("I must go down to the sea again, to the lonely sea and the sky/And all I ask is a tall ship, and a star to steer her by.") But in the 1970s it started to be used as an advertising phrase to publicize the "Tall Ships' Race" from Bermuda to New York, and people have been batting it around ever since. I really wish they'd stop. The term has no actual meaning.
Whenever I see "Tall Ship" in an advertisement or event announcement I start looking askance. (There was a "Festival of Tall Ships" here in NC a few years ago. I started feeling uncomfortable when I saw that title. When I found out that the organizer called himself "Captain Horatio Sinbad," I avoided the whole thing like a plague. It turned out to be a near-total flop.)
There. That's my curmudgeonly retired professor pronouncement for today. Bah, humbug.