The important feature of a vectored interrupt is that the device itself provides the interrupt vector address.
With non-vectored interrupts, all devices using the same interrupt request routine will transfer control to the same location, and the interrupt service routine will have to figure out which of the possible devices is actually interrupting.
With a vectored interrupt, the device tells the interrupt mechanism what its vector address is. The vector address corresponds to a store location in which the OS (or device driver) has written the address of an appropriate interrupt service routine. Typically each device has its own vector address so the "which device is interrupting" decision is trivial.
The terminology is a little messed up, since the table of interrupt service routine addresses is frequently called the "interrupt vector table", but the term used for both vectored interrupts (interrupting device identifies a slot in the vector) and non-vectored interrupts (interrupt request line corresponds to a slot in the vector).