​“Staphylococcus” is the common Staph infection. There are about 40 sub-groups (for example Staphylococcus Epidermis, Staphylococcus aureus, Staphylococcus Lugdunensis, etc.) and other Staphylococcus Sub Species.
The common Staph infection is just that—Staph. Staph is usually treatable with antibiotics. Not all Staph is necessarily bad.

For example, Staphylococcus Epidermis is on the skin. It is expected to be there. It is part of the normal skin make-up.
Staphylococcus fits into a group of bacteria called “L.A.B.” This stands for Lactic Acid Bacteria. Lactic Acid Bacteria are very common. In fact, yogurt is a Lactic Acid Bacteria. We have it in our stomachs and intestines.
Lactic Acid Bacteria are very simple to understand because they do the same thing over and over. They assimilate (eat) glucose, or sugar and it really doesn’t matter what kind of sugar.
They gobble up sugar all day long and when they are done the by product is Lactic Acid. Very simple.

CATALASE & COAGULASE:

Catalase and Coagulase

So,Staphylococcus bacteria is a type of Lactic Acid Bacteria

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SOURCE:
http://rightdietplus.com/2016/09/how-to-permanently-cure-staph-aureus-infection/