Voltage and resistance is all that matters.
For simple (non-reactive) devices like steppers/speakers/etc, the current is determined by a very simple equation:
current (amps) = voltage (volts) / resistance (ohms)
So, given a fixed voltage and the fixed resistance you can calculate amperage. It's that simple.
A Power supply with a rating for a certain amperage tells you a few things.
First, the power supply is only built to handle that amperage. Wiring, resistors, and other devices heat up based on more or less on much how current you put through them. A thicker wire heats up less, and can therefore handle more current without danger of melting or fire. This is because there's a larger cross-sectional area for the power to be distributed over. (although it's not quite so simple if the voltage has a high frequency AC component to it) So, you don't want the supply to go significantly beyond it's rated range. It may be built with thinner wire and burn up.
Second, many power supplies are fairly dumb devices (unregulated). If they're rated at 12V @ 1A, they may give you 16V at 0.25A, or 10V at 2A (if they don't burn up). You only know that you'll get 12V at exactly the rated voltage. This can give you problems if you put a 12V 5A supply on a device that only draws 100mA (it may end up giving the device 16V+)
Third, supplies also have an internal resistance. So: CURRENT = VOLTAGE / ( RESISTANCE_OF_LOAD + INTERNAL_RESISTANCE_OF_POWER_SUPPLY). So, the current it is able to supply to the load is limited somewhat by this internal resistance. Your 1.2A rated stepper example on a 650mA supply might only be able to draw 900mA for this reason. (For a stepper, that'd usually just mean it operates more slowly and has less torque)
Forth, the supply may have active current limiting. If your mentioned 650mA supply had current limiting, it may limit the maximum current (for safety) to 700mA.
The best power supplies are actively regulated. This means that a microcontroller or some feedback circuit is watching it's output and adjusting to always give you the rated voltage. They usually have current limits, too... so these are the safest type of power supplies. However, many are switching-mode power supplies instead of linear and may add noise, so they may be undesirable for certain devices (high performance audio comes to mind).
So... there's lots of factors that basically mean use a power supply that's close to what your load needs unless you know for sure that it's regulated. Never use a supply rated below what your load needs, unless you have a very good understanding of both the load and the supply and how they'd react to that.
Reactive devices (like microcontrollers) can dynamically change their resistance to suit their needs. Running these devices with less power than they need would usually mean some sort of incorrect operation.