difference of colours and saturation

So what app are you using on the phone? If it's a web browser, which one?

For laptops and desktop computers, over saturated images are typical (and inevitable) when using a wide gamut monitor, and using an application without color management, like the Windows 10 Photos app.

There are no color managed native applications on Windows, so with a wide gamut monitor, it's necessary to use a third party color managed image viewer, like FastStone, which is free for personal use.

Color management must be enabled under Settings > CMS, and both boxes must be checked.

To see correct colors on your laptop, calibrate it with a hardware calibrator, like an i1, ColorMunki or Spyder.

The calibration process also creates a custom monitor profile that describes your monitor accurately.

The monitor profile is used by color managed applications (like Lightroom and Photoshop) to display correct colors – colors are converted from the document profile to the monitor profile.

Note that native Windows applications like Photos, Paint, etc, are not color managed, and can not be expected to display correct colors.

Calibrating your monitor may require you to re-edit your images, which might make them display better on your phone.

What kind of phone do you have, and what app are you using to view images?

In my experience, most web browsers for Android display quite accurate colors.