I know some will disagree, but there is also a difference in tannins. Natural fruit tannins are usually felt mostly in back of tongue but not as much in cheeks. Oak tannins/wood tannins are more drying, astringent and are really strongly felt in the cheek.
And tannins are actually an acid as well, which explains where it might be hard to differentiate the fruit tannins from natural acidity.
(Tannin is really a generic name for large molecules with a central core of tannic acid. I won't bore you with the chemistry lesson.)
And what PH said, get some fresh grapes and chew the stem. Tannins (akin to fruit tannins).
As for wood tannins, I don't recommend chewing an oak stave.
And let's not get started on the different types of acids.