The most practical way to start describing a perfume is according to its concentration level, the family it belongs to, and the notes of the scent, which all affect the overall impression of a perfume from first application to the last lingering hint of scent.
Concentration levels
Perfume oil is necessarily diluted with a solvent because undiluted oils (natural or synthetic) contain high concentrations of volatile components that will likely result in allergic reactions and possibly injury when applied directly to skin or clothing.
By far the most common solvent for perfume oil dilution is ethanol or a mixture of ethanol and water. Perfume oil can also be diluted by means of neutral-smelling lipids such as jojoba, fractionated coconut oil or wax.
As the percentage of aromatic compounds decreases, so does the intensity and longevity of the scent created. Different perfumeries or perfume houses assign different amounts of oils to each of their perfumes. Therefore, although the oil concentration of a perfume in eau de parfum (EDP) dilution will necessarily be higher than the same perfume in eau de toilette (EDT) form within the same range, the actual amounts can vary between perfume houses. An EDT from one house may be stronger than an EDP from another.
Furthermore, some fragrances with the same product name but having a different concentration name may not only differ in their dilutions, but actually use different perfume oil mixtures altogether. In some cases, words such as "extrême" or "concentrée" appended to fragrance names might indicate completely different fragrances that relates only because of a similar perfume accord. An instance to this would be Chanel‘s Pour Monsieur and Pour Monsieur Concentrée.
For instance, in order to make the EDT version of a fragrance brighter and fresher than its EDP, the EDT oil may be "tweaked" to contain slightly more top notes or less base notes.
Olfactive families
Grouping perfumes, like any taxonomy, can never be a completely objective or final process. Many fragrances contain aspects of different families. Even a perfume designated as "single flower", however subtle, will have undertones of other aromatics. "True" unitary scents can rarely be found in perfumes as it requires the perfume to exist only as a singular aromatic material.
Classification by olfactive family is a starting point for a description of a perfume, but it cannot by itself denote the specific characteristic of that perfume.