Sorry for the delay getting back to you ( UK and US time zones I'm afraid ).
You are correct and the difference between the two is why they vary so greatly in size, a full recovery partition on an OEM computer unless previously formatted will normally have all of the required drivers, any pre installed OEM utilities such as diagnostic tools and unfortunately quite often a lot of bloatware such as basic games ( Wild Tangent comes to mind ) a Microsoft Office trial version and an AV trial such as McAfee to name only a couple, the downloaded ISO however only contains the Windows OS itself.
There can sometimes be more than one recovery partition present on a HDD which may explain the 512MB suggestion, if the ASUS notebook shipped with Windows 8.1 on the HDD unless it has been deleted or it is inaccessible for some reason there should be at least one other recovery partition on the drive, this could be around 20GB as it should contain all of the OEM software that I mentioned above, this larger partition is intended to be used for restoring the notebook to out of the box new and the facility is called ASUS Backtracker, the user guide for this can be found here
In essence a recovery USB thumb drive to access a non bootable computer need only be around 4GB but if you wish to create an exact image of a full recovery partition then the USB storage device will need to be much larger.
To create a recovery USB device and/or an image of what is on the HDD you can use a program such as Macrium Reflect (free) an Essexboy tutorial here.
You are welcome btw