In short, unless you have evidence to the contrary, you should assume that most of the carbon in a fossil is from contamination, and is not originally part of the fossil. The nuclear tests of the 1950's created a lot of C14.
Old samples contain much less C14, so the measured date of older samples is strongly affected by even small amounts of contamination.
The third kind are dates which were measured before the 1970's.
Some corals can be carbon dated, and also dated by another radioactive material, Thorium-230.
Pollen found in the Greenland icecap has been carbon dated, and also dated by counting ice layers. Trees grow a thick ring in a good year, and grow a thin ring in a bad year.
As the name suggests, fossil fuel is old, and no longer contains C14.
Both of these man-made changes are a nuisance to carbon dating.
The C14 will undergo radioactive decay, and after 5730 years, half of it will be gone. So, if we find such a body, the amount of C14 in it will tell us how long ago it was alive. The method doesn't work on things which didn't get their carbon from the air.
This leaves out aquatic creatures, since their carbon might (for example) come from dissolved carbonate rock.
Then, we have wood for which we know the right answer.
So, carbon dating has been calibrated against the rings of California bristlecone pines, and Irish bog oaks, and the like.
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