It is a confusing topic, and the answer is there really isn't a definition of what constitutes an extract. You'll see witch hazel extract, hydrosol, liquid, and juice, but they can all be the same thing.
The definition I have seen most is an extract is generally a distillation of the good things inside a botanical thing. (Wow, that was clear!) So for instance, say you buy some strawberry extract. It would be a powdered version full of polyphenols, flavonoids, vitamins, minerals, and so on in a purified and water soluble form. It could also come in a liquid form - water, glycerin, propylene glycol, or alcohol - and generally contains a preservative. They can be extracted in different ways, and it depends on whether the extracted stuff is heat sensitive, soluble in water or alcohol, and so on.
When it comes to things we see in our kitchen - rosemary, sage, green tea - the extracts differ in that they have been deodorized and standardized in some way. Green tea extract might contain 10% caffeine or rosemary 5% rosmarinic acid. (Always check to see what the standard is for the extract you are purchasing to make sure it contains the good stuff you want!) Adding a powdered extract is a way of guaranteeing you have the good stuff you want in the products you make.
In theory, you could brew up a pot of green tea or get the rosemary out of your pantry, but they would contribute smell and might cause spoilage. The extracts make it easier to add these great botanical ingredients to your products - if you added papaya to a toner, you'd have a horrible microbial infested mess in a week or less (even with preservatives). I mean, think about how long a crushed up apple would last on your counter! Instead, add some powdered papaya extract to a toner, and you have yourself a lovely creation suitable for normal to oily skin types.
And no, I don't know how some companies - not mentioning any names - can put "fresh" fruit into their products without spoilage or preservation (for the anhydrous products). I suspect extracts are the magic ingredient...