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@fforiwr I do know the answer to this one! Either "pawb" or "bawb" is fine, but in this case it's not a N/S difference. The soft mutation of "pawb" to "bawb" when addressing people is what I believe is called the vocative. It's just a little change to indicate that you are directly addressing people.
@Dewines Thank you! I may have just sat here saying both versions out loud, repeatedly, just to try and hear the difference. Much to the confusion of my dog 
@fforiwr bawb is short for "i bawb" /to All. The p changes to b after the word "i".
You can miss out the i, but "bawb" shows it is implied.
@Johnyoungc45 Ah! Thank you 
that makes perfect sense now.
@fforiwr As others have said, it's the vocative. I'm pretty sure it's dropping out of use in the modern language aside from fixed expressions, so it's optional nowadays - I, as a linguistics nerd, quite like using it! See: https://en.wikipedia.org/wiki/Vocative_case#Welsh
@Jhynjhiruu That’s a great example, thank you! Another reply told me it’s because it comes from “i bawb/to all” where the i is dropped but the b shows it’s implied. Which would also work for your sign above as it’s “To Students”. I love a good explanation!
@fforiwr i bawb would certainly have the same effect but in this case it really is vocative; think about calling out to someone: "Kids, please stop running" → "Blant, peidiwch â rhedeg" - you couldn't use "i blant" there.
@fforiwr
After certain letters p mutates to b.
@fforiwr According to Gareth King, soft mutation is applied :
"where a noun is used in addressing or calling someone – Dewch fan hyn, ºblant! Come here, children!"*
I'd been starting my e-mails to the other members of our little Welsh learners group with "Helô merched". Now virtuously changed to "Helô ferched" 
*Source: King, Gareth. Modern Welsh: A Comprehensive Grammar (Routledge Comprehensive Grammars) (p.14), Art. 11c. Taylor and Francis. Kindle-Version.
@janmakarta That’s brilliant, thank you! And thank you for including the example and citing your reference - things like that are a huge help 
@fforiwr Croeso, Kris! I've found Gareth King's books in general to be worth their weight in gold - and not at all boring, either; in fact he often has a refreshingly dry sense of humour, and 'Modern Welsh' is for me the definitive grammar book 
Pob lwc efo dy ddysgu!