So what would you call something like "it implements some common operations", like these?

For example, the Option and Result type both have functions like "map", they do the same thing just on different types. They're not quite generic in that sense, but on a high level they seem so.

Another example are reactive libraries. Everything is pegged into some common operations like map, take, and so on.

You're right, and I'd add on that monads only need pure and bind (>>=), das it!

    pure :: Monad m => a -> M a

    (>>=) :: Monad m => M a -> (a -> M b) -> M b

pure is sometimes called return and >>= is sometimes called bind and flat map.

I was unsure that bind was the same as flatmap but it looks like it is.

The "and_then" that they mentioned is the flatmap