Berries are a type of fruit. Like "fruit," "berry" has two fairly disparate meanings depending on whether you are talking the context of botany or in the context of food.
An indehiscent fruit derived from a single ovary and having the whole wall fleshy, such as a grape or tomato.
In the study of plants, the word "berry" means a botanical fruit that is all fleshy, was formed from a single ovary, and doesn't split open to release the seeds. Simple examples are grapes and tomato.
If you're not botanist, you really don't care about this definition.
A small, juicy, fleshy fruit, such as a blackberry or raspberry, regardless of its botanical structure.
This is what we would usually think of as a berry. They're small fleshy fruits which are usually going to be eaten whole. One would rarely eat a single berry.
There is surprisingly little overlap with the botanical definition. Blueberries are about the only thing I can think of that's both.
In practice, culinary berries are super easy to identify. We literally stick "berry" at the end of every one's name.