No and no.
in plain English, the language of the authors of the PHB, a berry is
a small, pulpy and often edible fruit. (Berry at WP, emphasis mine.)
Just like berry, "small" is not a defined term (when applied to objects--ignore creature sizes for a moment, please). But to paraphrase Potter Stewart "I know it when I see it, and this melon is not that."
The other 'no':
But as you say, berry used as a term of art includes watermelons. Today I learned it also includes tomatoes, cucumbers, eggplants, pumpkins, and bananas (ibid.). So, can Goodberry produce watermelons? Possibly. This depends on whether at your table the DM or the player describes the ambiguities in a spell's effects.
But you asked:
can the Goodberry spell be used to summon ten watermelons? (Emphasis mine.)
Even if a GM allows watermelon-summons, only one would appear because that's what fits in your hand. (And you'd have to eat the whole thing in six seconds to gain the effect. I'd rule you can, 'cause magic, but I'd want to see some serious RP involved.)