A DI converts an unbalanced, high impedance, instrument level signal to a balanced, low impedance mic level signal.
"Hi-Z" is short hand for "high impedance." Therefore, a Hi-Z input is meant for high impedance sources, such as an instrument output. Whether it does the same thing as a DI depends on the equipment itself and how it treats the signal once it's gotten past the input stage.
We usually refer to signal amplitudes in terms of dB measurements. These are only rough representations of what you might call an average amplitude and in practice, the actual amplitude varies considerably.
For instance, my active bass on full volume and at full boost is quite happy to output 4V peaks. However, my passive bass is lucky to get to 1V down hill with the wind behind it!
Generally accepted levels:
Consumer audio line level is -10dBu
Professional audio line level is +4dBu
Mic level is around about -50dBu but varies quite a bit from mic to mic.
Instrument level is a tricky beast to pin down, and the main characteristic that sets it apart from the others is that high impedance. I guess my passive bass is in the order of -6dBu but I wouldn't be willing to put that forward as a standard!