No: as I said above, an unhandled error generates an exception. But you shouldn't be able to have an unhandled error—good type systems prevent you from compiling such code, by treating all the errors that a function can return as cases you are required to handle at the call-site. Maybe generically with a default case, but you've still gotta handle them.

Dividing by zero is an exceptional situation (at the level of the processor, even!), rather than an error, because most divisions have known, nonzero divisors; certainly, all intentional divisions do. If you do end up telling the processor to divide by zero, it is assumed that you fucked up and didn't write your program right, because user-supplied divisors are a very rare use-case compared to known-domain divisiors, and a known-domain divisor being zero is indeed programmer error.

But, even if cases where the user controls the divisor are comparatively rare, they do exist. So, even if the processor isn't going to help you, why not have the compiler generate a check for them, such that integer division would be an (Either Integer Error) kind of operation? Well—performance.

Integer division—in languages where it generates an exception—is a low-level primitive. It's meant to be fast. (In fact, all integer operations in such languages are meant to be fast single-CPU-instruction-equivalent primitives; this is also why e.g. overflow isn't checked on integer addition.) Compilers for low-level languages are expected by their users to not generate any protective code for these primitives, because that protective code would get in the way of using the primitives at the highest efficiency possible. 99% of the time, the domains of these operations are fixed at the business level, such that these errors cannot occur. And, the other 1% of the time [like when writing a calculator program], the users of these languages use "safe math" libraries built on top of these primitive operations, rather than the primitive operations themselves.

Let me put this another way, with a concrete example.

In Rust, in safe code, you can't dereference arbitrary pointers, only opaque abstracted pointers (references) given to you by the runtime, that are guaranteed by the compiler to have non-null [direct] contents. You can make the inner type of a RefCell an Option<Foo> instead of just a Foo, and then it can be null... but this kind of null is an instantiation of the Maybe monadic sum-type, and so the compiler can notice when you aren't checking for its existence and stop you.

But in Rust, in unsafe code, you can dereference an arbitrary pointer, and the result can be null. What should happen when you do so? Well, that's an exceptional situation. You asked for unsafety, and then you did the stupid thing you weren't supposed to do. There's nothing that can really save your code now.

Before the invention of "exceptions", we just called these types of errors faults. Protection faults, for example. Your code would just be killed, without the ability to do anything, because it just did something that broke the semantics of the abstract machine (the process) that the OS had the program boxed up in. The OS might be kind enough to core-dump your process's memory in the process of killing it.

Exceptions are still faults. They just let you do arbitrary other stuff as your process comes tumbling down. There's nothing you, or the runtime, can do to "save" your process, when the "error" in question is precisely that you first asked your compiler for unsafety—asked it to not prevent your code from compiling if it does something invalid—and then you went ahead and used that unsafety to do something invalid.

In Erlang land, we have a third thing: exits. Exits are faults on a small scale—they kill the actor-process that generates them, and then spread across its linked siblings and parents to kill those too, until/unless one of them is "trapping exits", at which point that actor-process will receive the exit as an informational message from the runtime rather than just dying. Most actor-processes don't trap exits; and, in fact, you can't trap an exit generated by your own actor-process, only an exit "echoed" to your actor-process from below/around you. And the only processes that do trap exits, don't attempt to "save" the actor-process that is dying. Unlike with exception-unwinding, by the time an exit is "heard" by another actor-process, the actor-process that emitted the exit is already dead. The point of trapping exits is to decide what to do after the actor-process dies—for example, starting another one of the same actor-process to replace it.

(As it happens, POSIX exit statuses fit this concept as well, though semantics like bash scripts not being `set -e` by default kind of screws that up.)

Exceptions have their place—they describe a fault-in-progress, and let arbitrary things happen as a fault causes a stack to unwind, before the process dies. Exits also have their place—they let processes react to other processes having faulted. And errors have their place—they're a branch of the Either monad that a compiler can force your code to handle.

Personally, I don't see what confusion there is between any of these. They're roughly orthogonal.

And none of them represents "something bad happened from this function call. Somebody up there on the stack, help me recover, please!" (Those would be Lisp conditions, but nobody uses those.)