The Spyder4 is a colorimeter so technically the calibration software not only needs to know the panel type (background light type and/or active lighting technology) but also the exact monitor model.
Ideally, the software would also be able to interrogate the filter characteristics of the calibration device and your Spyder 4 seems to support this.
Long story short: Achieving inter-monitor agreement when using different monitor models is not easy which, IMHO, puts the whole calibration business to shame.
It is of course much better to calibrate than to leave (bad) monitors at their standards settings, but monitor calibration is no easy one-click road to happiness.
Have a look at these
DisplayCAL notes about colorimeter corrections to open up the can of worms.