But i asked the question what difference, in reference to the example of the C scale, not what can or cannot then be added or implied. Not what instruments it can or cannot be used on but what is the difference in the musical principal of showing a scale in tab or notation.

The answer is and always will be none.
No, the answer has never been none. The answer is that there's a vast difference. Tab does not tell you what note to produce, it tells you where to put your fingers. It assumes that you have your bass tuned one way, and it assumes that there is only one fingering. Standard notation assumes neither and is therefore both different and better.
A tab can never tell you the notes in a C scale because it doesn't work by notes. If your bass is tuned a certain way, and you follow the tabs, something that sounds like a C scale will come out. But by its very design, it doesn't tell you the notes, only the finger positions. That's what it DOES.
The late great Red Mitchell used to tune his upright in 5ths, C-G-D-A. For fun, imagine applying this practice to the EBG. If you do, you instantly render every single piece of tab written for a bass tuned E-A-D-G totally useless. You can't play a C scale from the tab. There is nothing from any of those tabs that you can salvage. You have to throw them away completely, or ignore them entirely, to play the music properly--thus defeating the purpose of writing them out at all. This doesn't happen with SN--no matter how you tune your bass, or how you produce your notes, you always know that you're supposed to produce, say, an A, and you know the difference between that and putting your finger on the 5th fret. It should be clear that this is in fact a very large difference in principle between the two.
Also, tab not only doesn't allow for alternative fingerings, it actually hinders you from considering them, which SN does not. To play a different fingering from what's on the tab, again, you have to ignore everything that's in front of you and come up with something else yourself. IOW, you might as well not have the tab at all. SN doesn't require this, because it doesn't specify fingering unless you want it to. An A is always an A. You see an A, you know how many different ways of playing that A exist, and you pick the one that works. No matter what fingering you use, the SN is still perfectly good and valid. Again, a vast difference in principle.
The point that tab is portable across instruments is not a small detail, it's a large one. That's why SN is a far better tool for teaching
musical principles, as opposed to physical actions on the bass. (Musical principles are precisely those principles that are NOT tied to the physical practice of any particular instrument.) I personally am not against tab for anyone at any time for any reason; not all of us have the same goals. There are all sorts of different ways of experiencing music as a spectator or a participant.
But the fact that we're sitting here in a bass forum, talking about general INSTRUCTION, suggests that we ought to be talking about fairly serious learning and thus fairly serious musical tools, which tab is not. If someone asks for instruction, it's much like asking for directions. If someone asks you the directions to some destination, are you going to give the route that is most likely to get the person there effectively, or the route that is confusing to follow, will take longer, and will quite possibly get him or her lost or stranded?