What is difference between DC current from dynamo and DC current from battery?
The dynamo voltage isn't constant at 12VDC.  It will vary depending on how fast the rotor is turning.
The dynamo probably can't deliver as much current as the battery.  Inverters need a lot of current.  Inverters step up the voltage. If you step up to 120V and need 1A of current, your inverter will have to draw 10A of current at 12V.
Even if the dynamo can supply the needed steady current, it may not be able to supply the sudden burst of current needed when the inverter starts up.  Inverters tend to draw a lot of current in the first moment at start up.  If the dynamo can't supply it, the voltage will drop for a moment.  The inverter will probably then shut off.