Since Babel 7 the Babel team switched to scoped packages, so you now have to use @babel/core instead of babel-core.
But in essence, @babel/core is just a newer version of babel-core.

This is done to make a better distinction which packages are official and which are third-party.

babel

Babel doesn't do anything,It basically acts like const babel = code => code; 
by parsing the code and then generating the same code back out again.

You will need to add some plugins for Babel to do anything like transpiling es6,JSX.

babel-core

if you want to use babel in your real project, you need to install babel but 
there's no babel package available.

   babel split it up into two separate packages: babel-cli and babel-core

   **babel-cli** : which can be used to compile files from the command line.

   **babel-core** : if you want to use the Node API you can install babel-
      core, Same as "babel-cli" except you would use it programmatically inside your app.

   use "babel-cli" or "babel-core" to compile your files before production.

before move on,

preset vs plugin :

We can add features(es6,JSX) one at a time with babel plugins(es2015), 
    or 
we can use babel presets to include all the features(es6) of a particular year.

Presets make setup easier.

babel-preset-es2015

babel-preset-env supports es2015 features and replaces es2015, es2016, 
  es2017 and latest.

So use babel-preset-env, it behaves exactly the same as babel-preset-latest 
 (or babel-preset-es2015, babel-preset-es2016, and babel-preset-es2017 together).

babel-preset-react

transform JSX into createElement calls like transforming react pure class to 
   function and transform react remove prop-types.

babel-polyfill

Without babel-polyfill, babel only allows you to use features like arrow 
 functions, destructuring, default arguments, and other syntax-specific 
 features introduced in ES6.

The new ES6 built-ins like Set, Map and Promise must be polyfilled

To include the polyfill you need to require it at the top of the entry point 
  to your application. 

babel-loader

you done with babel-core, babel-cli, and why need preset, plugins and now 
  you are compiling ES6 to ES5 on a file-by-file basis by babel-cli every time.

to get rid-off this, you need to bundle the task/js file. For that you need 
   Webpack.

Loaders are kind of like “tasks”, They gives the ability to leverage 
 webpack's bundling capabilities for all kinds of files by converting them 
 to valid modules that webpack can process.

Webpack has great Babel support through babel-loader

devDependencies

When you deploy your app, modules in dependencies need to be installed or 
your app won't work. Modules in devDependencies don't need to be installed 
on the production server since you're not developing on that machine.

These packages are only needed for development and testing.

Isn't there any single dependency to replace them all?

as you read the above states, You need some presets and loaders to transpile 
 es2015 or JSX files.

babel -> @babel

Since Babel 7 the Babel team switched to scoped packages, so you now 
have to use @babel/core instead of babel-core.

Your dependencies will need to be modified like so:

babel-cli -> @babel/cli. Ex:  babel- with @babel/.

@babel/core is the scoped package structure that was introduced in v7, so from v7 this is the only correct way to reference the package. babel-core is used in prior versions

babel-core is the API. For v5 the babel package is the CLI and depends on babel-core. For v6, the babel-cli package is the CLI (the CLI bin command is still babel though) and the babel package doesn't do anything. babel-runtime I guess is just the runtime (polyfill and helpers) to support code that's already been transformed.

AFAIK you need at least babel-loader@^8.0.0-beta to use babel 7+ with webpack. The stable version of babel-loader is still version 7. use babel-loader@next or specify another beta version of the loader to use.

Here is the latest version on the registry. babel-loader 8.0.0-beta.6

From the official babel docs:

Babel is a toolchain that is mainly used to convert ECMAScript 2015+ code into a backwards compatible version of JavaScript in current and older browsers or environments.

This means that you can write your code in a version that is not compatible in some browsers then babel convert you code to make those browsers 'understand' it. This process of conversion is called compiling.

From the official babel docs:

Babel comes with a built-in CLI which can be used to compile files from the command line.

This means that @babel-cli comes inside of @babel-core. It is a tool that helps you work with babel. It helps you compile you code using the command line interface.

Since Babel 7 the Babel team switched to scoped packages, so you now have to use @babel/core instead of babel-core.
But in essence, @babel/core is just a newer version of babel-core.

This is done to make a better distinction which packages are official and which are third-party.