They mean the same thing, which is tomato. You may know that tomato was not an plant originally growing in China. So in terms of 番茄, if you can separate the two characters: 番 equals to another character 蕃, meaning "other countries (as a noun)" or "from other countries (as an adj.)", and 茄 usually refers to egg plant, which belongs to the same plant family of tomato. About 西红柿，if you can also read these characters individually, you will see it means West + red + persimmon(this is an original species) . And you will see it also means the fruit/vegetable in a red colour from the west and it looks like a persimmon (persimmon is orange colour). So they are two ways of saying the same thing. And if you would like to know, in my hometown it is also 洋柿子, also meaning "overseas / foreign persimmon" PS. you may find the names for potato in Chinese interesting, too.

番茄 and 西红柿 are the same meaning in Chinese，The Chinese regard tomatoes as fruit as well as vegetables,It's just different people call it different names, so if you buy the tomato in supermarket,you can say "番茄“ as well as "西红柿”

There is no difference. 番茄 and 西红柿 are the same plant. Northerners are used to calling 西红柿，Southerners are used to calling 番茄。 But the tomato sauce，we only call it 番茄酱。

In addition to Zora's excellent explanation. 蕃茄 is an older term. 蕃 means "barbarian/barbaric" just like the original meaning of "barbarian" (non- Greek). The Chinese, like the Greeks, view other countries as less civilized and so has this negative connoation attached. 西 is a neutral term for "foreigness" Perssimons can be grown in colder climates but not egglants Hence the way of describing the same thing. On a side note, tomatoes are technically a fruit but LEGALLY a vegetable. The US Supreme Court has decided that it is a vegetable in 1893 in the case Nix v. Hedden because fruit are not dutiable whereas vegetables are!

有些地区的人叫它“酸梅”。