Which is better? The digital or optical stabilization? Are there any differences between them?
No question — optical. Digital image stabilization in video can mean clever frame-by-frame alignment, but on digital still cameras, it's just code for "cranking up the ISO so that higher shutter speeds are used".
In other words, it's marketing BS. Nothing is actually being stabilized, and it doesn't provide anything that you couldn't do yourself with a camera that allows control over ISO level and shutter speed. However, on cheap point and shoots, digital stabilization means that at least there is an automatic mode which biases towards faster shutter speeds. This will reduce motion blur (from either camera or subject movement), but since the actual light reaching the sensor is reduced and amplification increased, it will come at the expense of noise. And if you're in low light already, it will probably be completely useless.
Note that some people make a distinction between lens-based image stabilization and body-based sensor-shift stabilization, calling only the former "optical stabilization" — both of these are genuine and effective, with their own plusses and minuses. And neither is "digital" — so that's really a whole separate question. More on that at What is the difference between in-lens image stabilizing and sensor-based image stabilizing?