Essential oils are extracted from fruits, leaves, roots, stems, barks and or flowers. It can be steam distilled or cold pressed. Some companies use solvents to extract their oils. But in most cases they are carefully refined to preserve the very thing that makes them "essential". Even if an essential oil is natural, it doesn't mean that the means from which it was extracted was. Many oils made in this fashion are still labeled "natural or "pure", but I suppose it all comes down to what you personally define as "pure".
Essential oils are more expensive than Fragrance oils since it takes about 30-50 petals of a rose to make a single drop of rose oil and hundreds of pounds of plant matter could be used to make a single ounce of essential oil. Certain plants used to create essential oils such as certain types of sandalwood, cedarwood, and rosewood oil are now endangered from the over-harvesting.
Since we know that Essential oils came from our natural resources, it doesn’t mean that they are 100% safe and effective. There are those people that are particularly sensitive to fragrance oils, yet there are also some people that are sensitive to essential oils as well. You will also find that if someone has an allergy to a certain plant, the reaction may be exaggerated with the essential oil since it is a concentrated form of the plant material. Lotions or creams with Essential oils should be treated carefully. Too much of a particular oil can have far more irritating results than benefits. For example, if you make a lotion with large amounts of grapefruit, orange, or any other citrus, during hot and humid weather these citrus oils may enhance your chances of getting scorched by the sun or possibly an even worse reaction from sun exposure. Large amounts of rosemary essential oil or extract in a "leave on" product could cause massive irritation. Some essential oils are even toxic if ingested! You have to get to know your oils before using or experimenting new ingredients.
Fragrance Oils can be a mixture or combination of mixtures of natural and synthetic materials. Synthetic ingredients are manufactured through chemical process. These are "man made". Fragrance oils are a blend, often synthetic, of a number of ingredients usually diluted with an oil carrier. Fragrance oils are usually cheaper. Some oils can have adverse affects such as headaches and dizziness. This is due to them being impure or possibly synthetic.
There are famous and given much favor scents that can only be found in a fragrance oil. Some fragrances simply cannot be mimicked through essential oils. For example, there really isn't any cranberry essential oil.
Manufacturer of the fragrance oil does not have to disclose the ingredients used in making their fragrances because of what we call “trade secret”. This would ensure perfume or cologne companies would make their product different or distinct from their competitors. Basically you may never know what in the world is really in fragrance oil, but they do have guidelines in place to ensure the general safety of the product.
There are people that are particularly sensitive to fragrance oils and even sometimes just plain allergic to them. If a product is carefully made and the fragrance oils are carefully measured and added in the recommended amounts, the amount of fragrance actually used is generally unlikely to cause a reaction.