There are different types of fairies. That's just about it. Nothing more, nothing less. The fairies that follow the Kokiri around are guiding/advice/navigation fairies (like
Tinker Bell from
Peter Pan; although, she was also called a "pots and pans fairy" originally). These ones come in a variety of colors. Their ability
to temporarily change color can be taken as all a part of their ability to
guide (like a warning signal/light). The other ones are of the healing variety, and are primarily red in color (bar the games in which they aren't)—there appears to be a 'chubby' variety of this type as well. In addition, it is generally believed that a little humanoid fairy lies within the ball of glowing light; the blinding light obscures their true appearance. Great Fairies are 'fairy goddesses,' but
not in the Western sense (i.e., what us uncultured folks are used to), so let's not go there with that whole "
omg how can the be gods theyre not a tryfors!!!?!111one!" debate. The Queen of Fairies is their leader. To explain the difference in appearance of each type of fairy from game to game: graphics and design direction...bam.
Fairy variety has a basis in real-world myth
wherein a multitude of different classifications of 'fairies' can be found; there's evil fairies, good fairies, elemental fairies, healing fairies, fairies that don't even look like your traditional Western fairy, etc. etc. I wouldn't be surprised, however, if those things we call fairies in the games are something else entirely; they just so happen to bear the title of "fairy" for the sake of simplicity. Think outside of the box, but within the realm of reason.
Stuff.