The existence of fatty acids
Carrier oils contain fatty acids and will leave an oil stain on paper or cloth.
Essential oils don’t contain fatty acids and will usually not leave stains on paper or cloth. (Note: More viscous, darker-colored ones might because of their color.)
The reaction with plastic
Carrier oils are usually sold in plastic bottles. This is generally fine if they’re not stored for too long.
Essential oils, however, will dissolve plastic. This is one reason why reputable vendors will never use plastic packaging. They will use glass or metal instead to avoid oil contamination.
The rate of evaporation
Carrier oils are what we call fixed oils. They don’t really evaporate at room temperature.
Essential oils are volatile oils. They evaporate (diffuse) at room temperature.
The aroma strength
As carrier oils are extracted from the “fatty” parts of plants, they have very little aroma or at most, they will have just a slight nutty smell. If you detect a strong (and rather unpleasant) smell in your bottle of carrier oil, it probably means it has turned bad (see #7 below).
Comparatively, essential oils are made up of volatile compounds obtained from the aromatic parts of plants. Hence they have much stronger, and usually much more pleasant, scents.
The capacity to turn bad
Carrier oils turn rancid over time. And you can easily tell that they’ve turned bad from the smell.
Essential oils don’t turn rancid. But they do oxidize over time.
Oxidation causes all oils to gradually lose their therapeutic value and become less effective. Certain oils can also become more toxic due to oxidation.
Hence, both types of oils should be properly stored and used within their shelf lives.