How can i do the Export the JPG image same size as my psd file?

Export As Jpeg can scale images, convert colors to SRGB and strip meta- data. Defaults are 1x scale, convert to sRGB,  strip meta-data and not embed a color profile.  scaling should be constrained you resized image should have a 1:2 Aspect Ratio like your  600mm x 1200mm document. Its been resized to  871.36mm by 1746.25mm.  There may be a problem with export if your document is 600mm x 1200mm like you wrote.  The resized image  hast an aspect ratio of 0.498989898989899‬ it close to 0.5.   Also look at you Export As Jpg dialog

It could also be your image was not scaled just saved without any resolution setting. Export is used to save web image  and resolution is meaningless on the web only the numbers of pixels matters there. Opening a file without a resolution setting Photoshop would default to 72ppi photoshop needs to have a resolution setting for when you use units like inches or mm which is relative to print resolution

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This is filed under the category of "you can't have your cake and eat it too"...

Export will remove the print size and PPI metadata from the image (the pixel dimensions should be the same). This information could be added in using 3rd party software, however there is no need to do so.

Only save/save as will retain the PPI and print size metadata info.

When performed correctly, there is no reason why the colour should be different when using save as vs. export.