It's not the same as parallel compression though it can produce a somewhat similar sounding result.
In parallel compression you're basically squashing a signal and adding it to your original signal either on a parallel track or directly in a machine or plug-in using a mix or dry/wet knob.
Top: Original waveform
Middle: Parallel compressed result
Bottom: Regular compressed result (shabby job, I admit!) :-)
Notice how the middle result (parallel compressed) maintains the original peaks of the signal but adds fullness from the bottom and up, so to speak.
One of the benefits of parallel compression is that you're not touching the transients of the original signal. You can also further process the parallel signal with EQ or distortion for more radical effects. Mind the phase, so you may consider using linear phase EQ and full ADC/PDC in your DAW.
With upward compression or de-expansion (as used in the Flux plug-in Solera and Alchemist) you're processing directly on the original signal, bringing up the low level information.
The most interesting use of de-expansion is in the Flux Syrah which has the potential for threshold independent de-expansion. This is practically achieved by setting the Amount and Thickness parameter for 100%. I then recommend adding the result in parallel within the plug-in for a more subtle effect and more user control. I've written a guide somewhere on GS for that trick and it's included in the plug-in as the presets called Parallel Enhancer Soft & Loud. It sounds advanced (and it is) but not for the user, so check it out!
In the Flux Solera and Alchemist it's completely user controllable including both a ratio and range option as well as the threshold, of course. You can not underestimate how powerful that combo is since it allows you to potentially use high ratios in combination with low threshold (which would normally produce lots of gain changes) but keep the actual gain range to e.g. 2 dB using the range knob.