JPG different than RAW image

Raw Image are Mosaic images they are not a RGB image till you convert it  the into an rgb image is some color space  8bit or 16bit color depth and Adobe RAW Conversion engines has ways you can apply color adjustments. You the save a RGB IMAGE is some Image file format like Jpeg.  A RAW image can be developed many ways. You never see the Mosaic Image. When you see a raw image you are looking at one of the possible conversion that are possible,  An image may be converted many time and each conversion can look different then all the others.   A Jpeg image is a conversion of a Camera Sensor RAW data. Its a 8Bit RGB  images.  without transparency. When you view a jpeg you are viewing some conversion and when you view your raw file you are viewing a possible conversion not the mosaic image.

So, just to clarify, I am not complaining how my RAWs look, I am satisfied with those. I just want to know why my JPEGs don't look the same when I saved them in Photoshop. They turn out completly flat and murky.

No, they are not supposed to be the same. You misunderstand.

The jpeg is generated by the camera, using automated processing in the camera.

ACR is a completely different processing engine and the result will always be different. The default settings are intentionally conservative, because you are in any case supposed to make your own. You have full control and it's entirely up to you.

There is no such thing as an "original" or "true" version of a raw image. The raw file itself is just a very dark, very flat and tonally compressed grayscale image. It needs to be processed into a useful, recognizable image, and that processing is an interpretation.

It might be of relevance so I should add that the RAW is Nikon NEF image.
When I convert it to JPEG via online tool (www.iloveimg.com), the image stays the same (no change in colors whatsoever). So it must be something wrong I'm doing in Photoshop.