Photoshop :: Differences In Transferring Masks To Selection And Back

I make layer mask which is a bit fuzzy, so it merges picture from both layers in some parts. Then I want to save it in order to use it later somewhere, so I convert the mask into a selection. But the selection does not hold the fuzziness of original mask, so when I use it as a mask somewhere else, it varies from original.

I attached the psd file with example what I mean, I have saved mask of the Layer 1 as selection, loaded into Layer 2, created mask, but it is not the same, when I switch on and off visibility of the Layer 2 the picture changes.

Is there a way to make the selection to hold all the information about the mask including fuzziness exactly ?