Theoretically, a purpose-specific "speaker-output" (commonly called a "line-out") should have a fixed output level.
This is generally called "line-level", and if the piece of audio equipment (in this case your computer) is properly designed, the volume of the output should be fixed.
This is to enable you to feed the output into another device, typically an amplifier, that is designed to work with a specific input range.
This second device will then provide the volume control. As such, ideally, changing the volume on the computer should not affect the line-out signal level.
The signal out or line out remains at a constant level, regardless of the current setting of the volume control. Recording equipment can be connected to line out without having to monitor it through the device's speaker, and without the loudness of the recording changing if the volume control setting of the device is modified whilst recording.
As you can probably deduce, most consumer electronics don't bother to follow these guidelines, so in your case, it's likely that both outputs are functionally interchangeable for most purposes.
It is possible that the output impedance of one of the outputs is significantly different then the other. This would suprise me, though, as output buffers capable of driving typical headphones are very inexpensive, and it's good design practice to stick them on any outputs where an inexperienced user could conceivably plug a pair of headphones.