Yes that's the same sensor.
also, I do not have the money to buy the pre-made board as it costs $50. I don't know what to do :[
I have the Parallax CO2 board with MG811 for use at my workplace, we were characterizing it for possible use in a project. From my own investigations with it, depending on what you want to do with the sensor the board isn't necessary and might not be worth the extra money. The main purpose of the Parallax board is the an alarm function, the output is an alarm signal goes high if a manually set CO2 threshold is exceeded (the threshold is set using the board's potentiometer and a voltmeter). In order to achieve this the board also raises the original sensor signal's voltage from a 250mV to 330mV range to one around 1.8V to 2.4V; but this is only available on test pin vias, not through the premounted headers. In both cases the lower end of the voltage range means higher levels of CO2.
As stated earlier, if you don't want the alarm feature and would like a different voltage range (e.g. changed so it's range is closer to 3.3V or 5V and inverted so the higher voltage readings correspond to higher CO2 levels) the Parallax board is probably a waste of money. In any event, if you want to use this sensor with an Arduino you will need to change the signal's voltage level. Even using 1.1V as a reference it's difficult to get useful readings from the sensor's direct output and lower voltages are innately more prone to EMI issues.
I hope this helps!