Terminology: Dressing Oil, Anointing Oil, Condition Oil
In hoodoo terminology, touching a drop of oil to your finger and then placing it on yourself or another person is called "anointing." Drizzling oil, rubbing it, or touching a drop of it onto an inanimate object is called "dressing." (Other old synonyms for dressing are "preparing" and "fixing.") When a man rubs John the Conqueror Root Oil on his penis, he is anointing himself; when he rubs it on a red penis-shaped candle or a John the Conqueror Root, he is dressing them.
A "Dressing oil" (the term comes from the leather goods trade) refers to any oil used in dressing or fixing candles, mojo hands, leather, furniture, money, and other such items, while an "anointing oil" (a term that comes from the Bible) refers primarily to use on the body.
An "anointing oil" is definitely intended to be skin-safe for people (barring allergies), because the term is taken from the Bible. For instance, in Exodus 25, it is said in verse 6 that the Lord requires: "Oil for the light, spices for anointing oil, and for sweet incense" -- with the implication that the anointing oil is not the same as lamp oil or oil for the lights. This is further underscored in Exodus Chapter 29, verse 7, where the manner of using anointing oil is clearly stated: "Then shalt thou take the anointing oil, and pour it upon his head, and anoint him." That 7th verse is about as clear as it gets: the anointing oil of the Lord was safe enough to pour on the heads of old bald-headed Moses and Aaron.
"Condition oil" is a term found only in hoodoo and conjure practice; it refers collectively to all anointing and dressing oils that are utilized in rites, rituals, or spell-craft to address or remediate an unwanted condition or to bring about a desired condition.
"Formula oil" is another way of saying "condition oil" -- that is, a conjure oil, hoodoo oil, anointing oil, or dressing oil made according to a conjure doctor's proprietary formula.
Now, why are some hoodoo condition oils traditionally called "dressing oils" and others traditionally called "anointing oils"?
Well, it is my understanding that those conjure oils and hoodoo oils specifically intended to be used on the body or which are derived from or have analogues among the alcohol-based perfumes (e.g. Jockey Club Oil, which derives from Jockey Club perfume, or Cleo May oil, which has as an analogue Cleo May perfume) are generally referred to as "anointing oils" or "perfume oils," while conjure condition oils that do not have such analogues or are not thus derived, but which have specific uses in candle rituals for certain conditions and are not worn on the body of the practitioner (e.g. D.U.M.E. oil or Hot Foot Oil or Crossing Oil, tend to be called "dressing oils." The distinction is a fluid one, however (pun intended!) and you will find people referring to the condition oils collectively as "dressing and anointing oils" or, more simply, as "condition oils."