The difference between imitation vanilla extract and real vanilla extract is that imitation vanilla extract is a more pure version of the product. Real vanilla extract has many more adulterants and impurities.
Is your mind blown, gentle reader? Then please, let me explain.
The main flavoring agent in vanilla is called vanillin, which is a creative name that sounds more tasty than 4-methoxy,3-hydroxybenzaldehyde. Vanillin is a benzene derivative, with several different radical groups added to the basic structure.
If you've ever spent any time around trees, you know they don't care about you. In fact, they don't really care about much. There is quite a bit of academic debate about why plants produce chemicals: sometimes as a pesticide or herbicide, and sometimes as a way to store chemicals that they don't know what else to do with. In any case, creating a single pure product is not what plants are interested in doing. Imagine all those enzymes in the vanilla plant getting paid by the hour, and the boss really doesn't check in very often. Thus you get vanillic acid, where a hydrogen in the aldehyde group is replaced with a hydroxy group. There is also ethylvanillin, where the methoxy group is replaced with an ethyloxy group. There are, by some estimates, about 150 chemicals present in real vanilla extract, most of them slight variations on the basic formula of vanillin: a radical group taken away, added, moved from an ortho to a meta position, etcetera. All of these chemicals share the same basic structure and physical properties, such as being soluble in alcohol, but the slightly differing structure of all these chemicals gives a richer, more subtle taste to natural vanilla. It is the difference between a note played by a single instrument, and the note being played be an entire orchestra.
It is somewhat interesting that "vanilla", which is often used as a synonym for "plain" (amongst other things), can be such a complicated subject from a chemical and biological point of view.
It is also important to note that while the difference between vanillin and full vanilla extract might be of only aesthetic concern, the same principle applies for other plants. For example, the attempts to find the "active ingredient" of both the opium poppy and cannabis has led to finding single chemicals that don't provide all of the therapeutic benefits of the complete plant.