There are a couple of different ways that a RAW file may be transferred between LR and PS using Edit in Photoshop.
For a Canon or other RAW file (.CR2 for Canon .NEF for Nikon etc) then you can right click and select Edit in Photoshop (or Ctrl/CMD+E shortcut). This takes all of the edits that have been saved in the LR catalogue for the image and transfers them to Adobe Camera Raw (ACR) which is used to render the image into Photoshop (You will NOT see an ACR window or any other reference to ACR at any time while it renders the image into PS though). At this point the image will appear and be shown with the .CR2 extension if it was a Canon RAW. I believe that it is done this way for compatibility reasons, it is exactly the same as if you had used ACR to do the editing and opened the file into PS. Once you have finished editing the image in PS you hit the Save command (Ctrl/CMD-S), NOT Save As, and the image will be saved with the same filename as the original file, but either a .PSD or .TIFF file depending on the options that are set within the LR external editing tab in the Editing/Preferences controls. The .PSD/TIFF file is not actually created until you use the Save command. As well as file type the controls also allow you to select colour bit depth (8 or 16 bit) and colour space. The file will be saved with any layers kept intact (unless you manually flatten the image). The image file will also get all of the keywords, labels star ratings etc that are applied to the original RAW file. The original RAW file and the .PSD/.TIFF file will also be included in the LR Library and stacked next to the original RAW image.
Second instance is if you are using a newish version of LR but a much older version of PS, say PSCS or CS2/3. In this case the version of the processing engine in ACR is not compatible with the one in LR (unless you deliberately choose to use the old process version). In this case LR is used to render the image that is shown in PS rather than ACR. In this case the .PSD/.TIFF file is generated as part of the rendering process, and it will have the .PSD/.TIFF as the suffix rather than the .CR2 in the windows title bar. All of the things that apply to the first option regarding the associated information, importation to library and stacking etc still apply in this case. Hitting save also takes you back to the image in LR just as in the first case as well. Although in both cases the file will remain open in PS until you close it, saving the image again will also update it in the LR Library.
There are some instances I have found where although the process versions are supposed to be compatible there are problems when rendering the image. Normally this has been issues with CA and fringing corrections and other issues with very high contrast straight edges at certain angles. As it is not possible to get LR to do the rendering as it would in the second case it is possible to work around this by using the normal Export command. It is possible to use that to make a .PSD or .TIFF file at full size. This image can be automatically included in the library on generation, and there is also an option to have PS open the file automatically too. All of the file EXIF data is also transferred the only practical difference to option 2 is that the image is not automatically stacked. If you are using any version of LR with PSCS6 you should not really get this issue, as you will have the latest version of ACR. These settings can be saved as an Export preset for quick use should you find it necessary
So that is the basic options for exporting RAW files. I would not use the Open as Smart Object option unless you really know what you are doing, as it embeds a copy of the RAW file in the .PSD file. At this point you have two files, the original RAW that you may make further no destructive edits to at any time, and the .PSD/.TIFF file that started off as a copy of the RAW with all of the settings baked into it as they were at the time it was created.
Once you have the .PSD/.TIFF file back in LR you may do some more changes in LR, such as create a VC for different types of output, such as differing crops and print soft proof options. Or maybe you want to create a B&W version of the image, I prefer the LR conversion tools over those in PS. So what happens if you want to go back to PS to make a change there? Again you have two options.
First Open in PS. This allows you to open the .PSD/.TIFF file as it stands on the hard drive. This is great if you saved the image before you had fully finished it, and simply allows you to go back to finish working on the file. Or you may have thought you had finished editing but then notice something that needs changing. The file opens you work on the file in PS and when you save the file the image is updated in the LR library. Now if you have created any virtual copies of the .PSD/.TIFF file then all of those copies will also be updated with the changes that you made to the underlying file. This is great, and often what you want to do, the extra bit of cloning to get rid of something you originally missed would need applying to all of the copies anyway. Your .PSD/.TIFF files will still have its layers intact too.
Now you might only want to make the changes to one of your virtual copies (or you added LR edits to the "master" .PSD/.TIFF file) and not affect the other versions. At this point you might want to use the Open with LR adjustments option (you only get this when looking at non RAW image files). This then creates a newly rendered version of the file, with the LR edits incorporated into it. compared to the original .PSD/.TIFF file this one will have been flattened in order to render the LR adjustments to it. I have never actually used this option to transfer a file from LR to PS as my workflow is LR -> PS (if necessary) -> LR (for final output). I have yet to have a situation where I have had to take an image out to PS then back to LR then make adjustments then out to PS again for work including the extra LR adjustments, so not too sure on the exact situation regards stacking and all those other things.
I hope this is of help, it is a bit long, but then it is relatively complex but seemingly a poorly understood relationship.