Since we get this question a lot we decided to write a blog post about it! The easy answer is that NO they are not the same, the difference is simple. Essential oils CONTAIN terpenes and a bunch of other compounds. Terpenes contain... terpenes. That's it, they ARE the compounds. Essentially terpenes contain only themselves, terpenes.
Terpenes are these amazing building blocks of scent and flavour, they give lavender its scent (linalool) and pine it's scent (pinene) etc. They are safe to ingest in appropriate doses when considered food grade - which is of course what our terpenes have been tested and .
Essential oils are hydrophobic, volatile compounds acquired by processing plants. They aren't something safe to be ingested unless under the strict guidance of a trained aromatherapist - and even then it should not be long term.
Since EO's use the entire plant extract it will contain terpenes as well as other compounds and hydrocarbons. With terpenes they are typically isolated then added to create specific profiles (like Blue Dream or Grapefruit Haze) or purchased isolated completely and used alone (like Limonene, or Linalool).
Another difference is that essential oils require a lot of raw materials. According to Earth Science Journal, in order to produce 1 pound of lavender essential oil, a total of 250 pounds of raw lavender is required. Terpenes do not need nearly this much raw material to be extracted.