It seems like no one wanted to answer the original question...
The main "difference" is that in a typical operation, you should have no current flowing into your AC neutral while all the current is flowing into your 0VDC ground.
Depending on your circuit these may be connected, but it's definitely not common practice. It's something that you should avoid unless you fully understand the circuit as well as what you're doing with it. In the case of a "basic" full bridge rectifier, the neutral on the AC side is separated by a diode from the DC ground; therefore there is a voltage drop there.
As far as making that connection to a PLC, I would highly discourage it. A typical panel design will have a 110VAC (or 220VAC) section which will have your phase and neutral buses. The phase/neutral would go into a 24VDC power supply which would then feed a separate 24VDC/0VDC terminals.
Is there a particular need as to why you'd want to connect these two?
Hope that helps...
Vlad