The difference is how the data is 'packed' onto the disc however it is not a case of compressing the data.
In the 'old' days, data was stored on a disc in concentric rings. Each ring held the same volume of data for example 1024 characters (don't take this as gospel, it is a long time ago and my memory is going). The number of 'rings' was dependent upon the drive mechanics. One drive may have catered for 10 'rings', a different drive may have catered for 20 'rings'. Although the physical size of the discs were the same the actual amount of data able to be held on the disc was dependent on the dive mechanics used. The 20 'rings' are closer together than the 10 'rings', so the mechanics for the 20 'ring' drive have to be finer. Once a disc was initialised by a particular drive type (10 or 20 'rings') it could only be used on a drive with the similar mechanics unless it was initialised again (when the information is lost).
With the new drives and memory cards, they contain the drive mechanics and disc (or equivalent in the case of SD type cards etc) within the unit but the concept is the same but the amount of data per 'ring' is now much greater. The mechanics for the 500GB Hard drive has half the number of 'rings' compared to a 1TB Hard drive, it is all about how close together the 'rings' are.
I have written this as if there is only one 'disc' (or platter) but apart from floppy discs there are in fact a number of discs (platters) mounted one on top of the other.
Think of a disc like a vinyl LP record but where the LP record has the data (music) recorded as one continuous grove that starts on the outer edge and spirals into the centre, the computer disc consists of numerous concentric 'rings'. The drive mechanism controls moving the read/write (and erase) heads from one ring to another.
Hope this hasn't added to the confusion