I agree on the first two 100% not too sure about how to define Freeskiing tho. When you read description of skis or look at websites they are classified into those catagories. You have Freestyle skis, Freestyle pow skis etc... Then you have Freeride skis which are more directionally inclinded etc. So yes I agree if youre on a Freeride ski you are probably not on rails all day and are more likely looking for the steeps.
I guess Freeskiing is the general term used for things not racing or things in that kind of catagory.