Fixed point integers vs. floating point "real" numbers are concepts from computer science, and can be researched e.g. on Google for free.
Nevertheless, a small overview:
- A fixed point integer contains n bits. It is roughly possible to use a fixed point integer to represent any value in the range -1 * 2 power ( n - 1 ) to 2 power ( n - 1 ) - 1. If the integer is unsigned, it is possible to represent 0 to 2 power ( n ) - 1. Therefore 24 bit signed integers give you -8,388,608 to 8,388,607 in increments of 1, while 32 bit integers give you -2,147,483,648 to 2,147,483,647.
- A floating point integer has 2 components: the base or mantissa, and the exponent. See http://www.math.byu.edu/~schow/work/IEEEFloatingPoint.htm]IEEE floating point description for details on the format. A 32 bit floating point number can represent more distinct values than a 24 bit integer, but less distinct values than a 32 bit integer. However the values of a floating point number are most precise around 0. (Which, IMHO, makes perfect sense for the digital audio world, which requires higher precision close to 0dBFS than it does at at noise level. Whether or not audio software makers take this into account though, I can't testify.)
Another thing to consider when reading specs is that the underlying library algorithms are absolutely crucial to determining the specs. Huge libraries of signal processing mathematics functions have been written specifically with floating point (and, in some cases, integer) in mind. This determines the route which many companies will take in writing digital signal processing routines, which are all inherently math-intensive.
Generally speaking, signal processing on (native) personal computers is much more efficient using floating points -- because dedicated floating point coprocessors do all the work. However memory and especially bus bandwidth considerations are also factors in deciding what format to use.
When you get into dedicated digital signal processor chips (e.g. made by Analog Devices), a lot of research and development has gone into libraries which are
not at all general purpose, and therefore numeric calculations will be done using whatever data format (int / float) the chip manufacturer has chosen to optimize.
All of this is interesting from a computer science point of view. But for the most part it is just marketing crap in the audio world. If you can hear the difference between 24 bit integer audio data, 32 bit floating point audio data, and 48 bit integer audio data, in a blind taste test, then you have much better ears than I.
$0.02,
Johann