From the manga and anime, as well reading their description on Fairy Tail wiki, Fairy Law and Fairy Glitter seem very similar.
When activated, a bright light envelops the area and inflicts massive damage on whoever the caster perceives from their heart as an enemy, leaving friends and bystanders completely unharmed.
it is a Magic that rivals Fairy Law and is a radiance of merciless light that denies the existence of nearby foes.
What is the exact difference between these two magic spells?
Fairy Law seems to only works on people who are your enemy and is an area of effect type of spell. This spell seems to draw from the user's internal power.
Fairy Glitter seems to be a single target type of spell. This spell seems to draws power from external sources (sun, stars, moon).
As an addition to Krazer's answer,
Fairy Law only affects a mage and any other enemies of the caster. The caster can't choose who will get struck by it. (Laxus tried to attack other Fairy Tail members but failed because his heart still considered them as friends.)
Fairy Glitter affects a single target whom the caster chooses.
This is my understanding:
Fairy Law is a magic that judges - it’s some sort of “punishment” or judgment, dead is one of the consequences but not the only one (can also be something like purification)
Fairy Glitter is a magic that “kills”or “destroy” on the other hand (which is the reason why Mavis keeps this spell to herself I think), it is more like a nuke or absolute power that wipes out the target’s existence;
So three of the spells: Sphere to protect, Law to judge, Glitter to kill.
Fairy Law — depends on who's casting it. The more power they have, the wide the range. It won't also have a lot of effect on people who are on the same level or have more power than the caster. Makarov was miles ahead of José when he used it on him .
Fairy Glitter — it's more focused than Fairy law, and the same rules probably applies to it. Unlike Fairy Law, only one person seems to have access to it at a time, and it doesn't have to be the guild master.
Fairy Sphere — it's the best defensive spell out of the three and was able to keep out Acnologia.
