Essential oils are aromatic extracts obtained from plants, often through distillation or expression. Fragrance oils are formulated blends that can contain synthetic aroma materials, naturally derived ingredients, or both. An essential oil describes a type of plant extract; a fragrance oil describes a prepared scent formula.
An essential oil reflects the aromatic materials available from its plant source. Fragrance oils give perfumers a broader palette, including impressions such as cake, fresh laundry, or ocean air that do not exist as straightforward essential oils.
A fragrance oil can also contain essential oils. Seeing a natural ingredient listed does not mean the whole formula is an essential oil, and a familiar scent note does not necessarily identify the ingredient used to create it.
For wax melts, the useful question is whether the formula performs well when warmed. For a room spray or diffuser, the requirements are different. An oil intended for one application should not automatically be used in another.
As a shopper, choose the finished product for its intended use and the fragrance you enjoy. Neither label by itself guarantees better scent, longer life, or suitability for everyone. 'Natural' also does not mean a concentrated oil can be used anywhere without following directions.
If you are comparing two finished home fragrance products, read their descriptions and use instructions. That tells you more about the experience you can expect than treating essential oil and fragrance oil as a simple quality ranking.