Tomatoes are vegetables under any classification scheme.
Nope, tomatoes are technically fruits, though they are commonly considered vegetables.
Just like pterosaurs are technically not dinosaurs, but are commonly considered to be in our culture.
Tomatoes are quite obviously fruits. Most of the industrial tomatoes are tasteless because they're harvested well before they're properly ripe, but a ripe tomato harvested at the appropriate time is obviously (and tastes like) a fruit.
It's almost as if vegetable is an overly broad (and as such not particularly useful) designation in the common lingo, much like dinosaur ;)
Fruit is a botanical classification (at least the way you're using it) whereas vegetable is a culinary one.