The translation is inaccurate.
It means safety in the same way as the salvation of the soul for Christians, but in a non-religious way, and applied to all of society. Yes, they were both quite grandiose in their wordings and full of themselves.
Safety, as it is commonly used, would better be translated, in French, as "sûreté". "Salut" would be a much, much stronger word.
But I'm still not quite sure what the French word "salut" means. Is there not a simple one-word English translation? What exactly is the remit implied by the name Comité de salut public?
Exactly. "Committee of Public Salvation". Sounds weird.
So, in this case, considering they considered themselves the defenders of the greatest ideology of all time and the (worthy) people, and were at war with both foreign countries and some of their own people, I’d say it'd mean something like:
"Committee in charge of delivering the country, the Republic (the idea of Republic itself; not just it’s French incarnation) and freedom / democracy (even though they weren’t quite democratic) from utter ruin and certain doom"