it seems you are already confused while teaching... And main thing is last one interrupt in haedware interrupt is not only INT its INTR i.e. Interrupt Request...
Handled by microprocessors itself. Hardware interrupts are manually give and are non changeable and software inter. Are coder friendly! Can be modified.
'INTA' stands for Interrupt Acknowledgement, as u might know. It means, microprocessor has accepted the interrupt request. So, it isn't an interrupt signal.