Pet Gems are not offensive or defensive, they are all of the same type and are of a purple color, containing bonuses which shall increase both your offensive and defensive stats.
You shall be able to equip two different types of Pet Gems into the two Pet Slots.
An overview of these gems can be seen in the image below, detailing the name, level and bonus of each gem. Due to the large amount of Pet Gems, these Gems are displayed with two rows for each level.