They are simply samples in different formats. EXS24 is used by the EXS sampler from Logic, Halion is from Steinberg, Kontakt is from Native Instruments, Gigasampler from Tascam etc. Most of them are self-explanatory. ACID is a format used in wav files - if you sequencer or player can read Acidized wav, it gives the added ability to manipulte tempo and pitch - great if you are into loops.
It is best to get samples in the format your sampler reads as that gives the best results. For example, I use Gigastudio. I only get Giga format. In the event when some libraries don't have the giga format (eg Symphony of Voices by Spectrasonics comes only in Emu, Roland and Akai) - I can get Akai format and Giga converts it. But as much as possible, all my samples are in giga format.
If you are using an Akai hardware sampler, then get Akai. Wav samples comes only with the raw wav files. They are not formatted and therefore will need a lot of programming to get it to work well (hence they are always cheaper). The sample formats don't just play one sample - the programming is very important. For example, the programming may include things like key-switching (ie pressing certain keys - usually lower registers - will trigger certain samples), round robin (playing repeated notes trigger different samples and so give more variation to your sound and getting rid of the "machine-gun" effect), release trigger (afte releasing a key, it triggers another sample). All these cannot be programmed in wav format. The wav format will give you all the articulations, but as you can imagine, to make it work well, you'll have to program each articulation yourself. Only get wav if you want loops (and if possible, get acidized wav).
