Voltages are differential -- they are the difference in electric potential between two things. In the case of a battery or power supply, the output voltage is between the + output and the - output. You can hook many things in parallel to these two output terminals, and each thing will see the same differential voltage.
As to the drawing, your AND gate will have 5 terminals. The two inputs, the one output, a power input and a ground input. For an AND gate structure, the output power does not come from the input, it comes from the power supply. So redraw the circuit to show the AND gate horizontal with its output driving the motor + side and the other side of the motor going to ground. And draw the AND gate with power and ground terminals shown. You should take the 2nd input to the AND gate up to the power supply through a pullup resistor, or I suppose you could pull it straight up like you are doing now.
BTW, logic gates do not have enough power output capability to drive real motors, not even small ones. So I'll assume that the AND gate symbol shown in your figure represents something more than just a 74AC08 type gate...