An EO is an essential oil. It is a natural derivative.
An FO is a fragrance oil, a man made oil. When said man makes that oil, he *may* use the EO as one of the ingredients in the FO or it may be 100% synthetic.
The main diffrence is that Lavender EO will have the medisimal(SP) value of the plant it is extracted from. It will cause relaxation. The FO Lavender, because it is man made will have no medisimal(SP) plant value.
EO's cost much more than FOs but you use way less. A good Lavender EO you may only need a few drops to scent 8oz of lotion while you may need 1 tsp of FO to scent that same lotion.