Half the point of using voltage, current, and resistance is that we don't have to care about what the power supply and resistor are made of. Whether you're using eight 1.5 volt AA batteries in series or one 12 volt car battery, if you connect 150 ohms across the terminals you will get about 0.08 amps. (The batteries have some internal resistance, but it's very small.)
It might help to look at this from a physics perspective. You have an electric field that pushes electric charges around, giving them energy in the process. That energy is then lost as the charges move through a medium. (More specifically, moving electrons collide with atoms.) The rate at which the charges move depends on both the strength of the electric field and the medium's ability to let the charges move around unimpeded. It turns out that the medium can often be described by a single parameter called the conductivity. This gives a simple relationship, known as Ohm's Law:
$$\vec{J} = \sigma \vec{E}$$
where \$\vec{E}\$ is the electric field strength and \$\sigma\$ is the conductivity. \$\vec{J}\$ is called the current density, and represents the rate of charge flow. This is a microscopic relationship. Note that the current and E-field are vector quantities. Doing physics with 3D vectors is a lot of work, but fortunately we have a simpler option -- circuit theory. In circuit theory, we talk about voltage (energy) instead of electric field strength (force). Just as in basic mechanics, this lets us deal with complicated situations in simple ways.
To make the jump to circuit theory, we have to change to using macroscopic variables. Instead of talking about the electric field strength at every point, we talk about the energy difference between two points. Instead of talking about the conductivity of a medium, we talk about the conductance of a physical object. Instead of talking about the density of charge flow, we talk about the total current through a wire. Now we can use Ohm's Law in its macroscopic form:
$$I = GV$$
where V is the voltage (energy per unit charge), G is the conductance (measured in amps/volt, aka siemens), and I is the current.
You can think of the voltage as being a sort of pressure that pushes charge through a circuit. The conductance tells you how much current you get for a given voltage. Now you're probably thinking "Where the heck did conductance come from? I was asking about resistance!" Well, resistance is just the reciprocal of conductance:
$$R = \frac{1}{G}$$
Resistance is more convenient because we're usually more interested in low-conductance elements in a circuit. With resistance, we can use a normal number like 150 ohms instead of a tiny fraction like 0.00667 siemens. This gives us the most familiar form of Ohm's Law:
$$V = IR$$
Now, back to your question. The reason that one car battery and eight AA batteries have the same effect on your circuit is that both of them are producing similar electric fields. Here's an analogy -- pulling a wagon over a rough surface. It takes a certain amount of force to make the wagon roll at a certain speed. It doesn't matter whether that force comes from your hand or a car engine -- it's still the same force.
