Differences between interruptions and exceptions

What is the difference between interruption and exception-general Linux technology-Linux technology and application information. The following is a detailed description. The interruption mainly responds to the hardware device and can return the events that were previously done before the interruption.
Exceptions are mainly used to report errors during command execution, such as a division of 0 and memory access error.

The interrupt has its own process context. The original process context remains unchanged, and the exception does not have its own process context. The process context of the current process will be used!
I wonder if the above understanding is correct? Can I report a hardware error?