Is there a difference between speaker and headphone jacks/ports?

It depends on what hardware you have in the computer, but there usually is a difference between speaker and headphone ports - specifically, relating to the max/min speaker/headphone impedance values you can use with either port.

Certain sound cards, for example the Auzentech X-Fi-Forte, include a built-in headphone amplifier on the headphone port. Taking a look at the actual output port specifications, we can also see different loading levels for the headphone and other line-out ports:

Headphone Load Impedance: 16 - 600 Ω
Line Output    Impedance: 330 Ω
Line/Aux Input Impedance: 10 kΩ  (10,000 Ω)

This is why many sound cards specify to not use a passive (i.e. unamplified) speaker with certain ports, as the lower impedance may cause too much current draw, and possibly damage the particular port.

The general thing to note here, though, is impedance matching your speakers/headphones to the appropriate port, and in general, your speakers go to the speaker port, and your (unpowered) headphones go to the headphone port, precisely for the reasons outlined above. This also explains why you might notice a slight difference in the volume levels between the two ports.

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.