What is the difference in meaning of a voltage signal and current signal?
For a signal, generally one of voltage or current is what is being controlled, and the other is a bi-product that is dependent on the load.

Consider a normal digital logic signal running between two CMOS chips on the same board.  That's a voltage signal.  Only the voltage is specified.  Not only is the current not specified, but it can vary hugely and isn't known by the designers of the transmitting chip since it depends on the load the receiver presents.

If the only receiver in the above example is a CMOS chip, then very little current will flow in steady state.  The load is almost purely capacitive, so current will flow in short blips when the logic level is changed.  If instead this signal drives a LED and resistor so as to light the LED when high, then the current will be very different from the previous case.  It will again be very different if the LED is wired between power and this signal (lit on logic low) instead of ground and this signal (lit on logic high).

Sometimes the signal value is encoded in the current, in which case the voltage ends up what it ends up.  A common example is the industrial 4-20 mA sensor standard.  The data is encoded by allowing from 4 to 20 mA to flow, but the voltage can vary over a range.  In fact, this is called the compliance range, with a larger range allowing for more flexible use of the device.  In this case, you can't look at the voltage to get the value being transmitted.