OK then Arty - I think it would be to your advantage were a few things to be clarified/cleared up at this point.
When you edit a RAW file in Elements you are in fact utilising the camera raw plug-in that is associated with Elements - so called ACR or Adobe Camera Raw. You are not using the bulk of the Elements application itself.
ACR, or Adobe Camera Raw is non-destructive as you are not editing at the pixel level so whilst you may feel that you are editing your RAW file, in fact you are not. ACR, via it's engine, renders a preview from the data contained within the raw file. At the same time it generates a second file - an xmp file - that links to the original raw file and contains any adjustments that you make. If you want to try a little experiment - on a raw image bring up the hue/saturation to a ridiculous level, say a horrible bright red. Now close down Elements and take a look in the folder on your PC containing the original raw image. In that folder locate an xmp file that has the same name/number of the original raw file e.g. original raw file 00001.NEF, xmp file 00001.xmp. Now delete that xmp file and when you open Elements one more you will see that the adjustments you made to the image are now gone. So, just to summarise - editing a raw file in Elements camera raw plug-in (ACR) is non-destructive with any adjustments etc being saved in an associated xmp file of the same name.
All cameras initially capture raw data whether they be called Nikon .NEF's or Canon .CR2 files. By the way, raw isn't an acronym for anything as often assumed - you shouldn't use the term as you would raw meat for example. Anyway, following capture of the data, if you have chosen to shoot in raw format then the captured data is saved unprocessed to the cameras memory card. If you choose to shoot in JPG format the raw data is still captured but this time the camera processes this data (much like a high street shop) and produces a JPG file to a standard or quality determined by the camera manufacturer (sometimes also user adjustable settings are provided) and in doing so compresses the file which is much smaller than the file would have been had you chosen to shoot in raw format. Part of this compression process is to discard luminance data in lieu of colour data which in turn places restrictions on what can later be edited in additional software i.e. Elements without further degrading the image.
Coming back to editing raw files again. Once you have finished editing to the degree allowed for in ACR you now have to decide do further edits need to be made. For example, if you wanted to replace a sky with one from another image you are not able to do this in ACR but instead now need to edit at the pixel level and this is where the bulk of Elements (and other applications) come into play. In order to do this you need to save out the data in a format that Elements can recognise and, equally importantly, without degrading the data in the process. For this the 16 bit TIFF format is a good one because it is a lossless format. What's important to realise here that if you decide to send a TIFF file into Elements for further editing ACR creates this TIFF file using the data from the raw file and also the edits which have been stored in the xmp file. Even though you have now created a TIFF file the original raw file remains the same meaning you can always go back to it at any time editing it in any number of other ways. This is the prime reason for always keeping your original raw file and for security reasons a backup is also advisable.
In Elements you are now free to edit this rather large TIFF file replacing the sky say as I mentioned this earlier. One advantage of TIFF files is that you have the ability to save this now edited file including any layers that you may have created. In this respect it is the same as a PSD file although PSD files are usually slightly smaller in size. The prime difference between the two formats is that TIFF is an international standard allowing you to open the file in any application capable of reading the TIFF format, which is most, whereas the PSD format is an Adobe format and generally speaking only readable in an Adobe application.
So, now you've got to the stage where you've carried out non-destructive editing to the original raw image (term used loosely of course - remember xmp above?), have decided that pixel editing now needs to be done at maximum quality and have saved out a TIFF file. Now you have to decide what's the intended destination or purpose of this produced and edited TIFF file. If it's destined for an on-line printing service who generally only accept JPG files with the sRGB colour profile you will now need to save out a JPG copy of this TIFF file.
Finally comes the decision process. Bearing in mind that you always have the original raw file to go back to what are the chances of you ever revisiting the TIFF file to carry out further edits? If the answer is non or highly unlikely then get rid of it, if not sure or maybe then retain it. For example, for the forums weekends competition I usually start off with a raw file, edit this and then save out a TIFF file should further pixel editing be required. I then save out to a JPG file for submission to this site. However, it might be the case that I notice a glaring error in my submission prior to the close of submission that only requires a quick and minor change to a particular layer. Retaining my TIFF file allows me to return to that particular layer, make any adjustments and save out to a new JPG file to replace my original submission prior to the closing time. Once that time comes and passes I then delete the TIFF file in the knowledge that should needs be I can always return to the original raw file and start all over again.
This has been a somewhat long post - longer than I originally intended, but I trust that somewhere within it you will find some useful bits.