They’re both. The term vegetable can mean either a part of a plant that people eat, or in a culinary sense it can refer to savory plant based foods that excludes things like grains, legumes, nuts, etc. In either case tomatoes, being both an edible part of a plant and savory gets to be a vegetable.
On a different level, botanically, not only is it a fruit, but it is a true berry.
So yeah, it can be, and is both things depending on the how you’re looking at it.
I don’t even know what “savory” means. What does that mean. I see it all the time but it means nothing to me.
Savory is the English term for the fifth flavor, often called umami. Savory foods have a distinct flavor different from salt, sour, bitter, and sweet. Sometimes described as “meaty.” Other high umami foods include soy-based foods and mushrooms.