At least the first two are also conflated in a typical CPU’s trap/interrupt/whatever-your-architecture-calls-it model, which is what Unix signals are essentially a copy of. So this isn’t necessarily illogical.
Sure. What I meant is, a CPU’s trap/interrupt mechanism is very often used to signal both problems that arise synchronously due to execution of the application code (such as an illegal instruction or a bus error) and hardware events that happen asynchronously (such as a timer firing, a receiver passing a high-water mark in a buffer, or an UART detecting a break condition). This is not that far away from SIGSEGV vs SIGHUP.
Some things (“imprecise traps”) sometimes blur the difference between the two categories, but they usually admit little in the way of useful handling. (“Some of the code that’s been executing somewhere around this point caused a bus error, now figure out what to do about it.”)