You use safety more in relation to correctness aspects of algorithms. Some safety properties you can actually prove. When it comes to robustness it is more about dealing with things sometimes being incorrect regardless of the safety mechanisms. So, a try catch for something that isn't actually expected to normally fail makes you robust against the scenario when that does fail. But you'd use e.g. a type system to prevent classes of failures as safety mechanism.

It's a very soft distinction, I agree. And possibly one that translates less well to the physical world where wear and tear are a big factor for robustness. You can't prove an engine to be safe after thousands of hours. But you can make it robust against a lot of expected stuff it will encounter over those hours. Safety features tend to be more about protecting people than the equipment.