In the US, DX most often refers to a foreign country no matter how far the distance. I live near Seattle Washington and the nearest foreign country is Canada, about 100 miles distant from my QTH.
However, DX has some specific definitions created in support of various contests and awards. For example, the DXCC award sponsored by ARRL recognizes a DX contact as a contact with a DX entity outside of your QTH entity. All recognized DX entities (not necessarily countries) are defined by ARRL for this very purpose. Also, there are several contests where the contest rules define what DX contacts generate points in the contest. Often these are the same as the ARRL definitions.
And, a DX entity is not necessarily a foreign country. For example, two of the states (Alaska and Hawaii) of the US are DX entities separate from the one I have in Washington state. Therefore, they qualify to be counted as DX. Actually, both Alaska and Hawaii are easy everyday contacts for my QTH (near Seattle, WA).
Should you answer CQ DX if you are not DX to the caller? I do that only to offer a signal report and in CW this can be done very fast. In response, I will say something like "579 WA K7PEH". But, I will only do this for someone who is distant from me, such as an east coast QTH trying for DX such as Hawaii or Alaska or Japan, etc. Some ops get upset if you answer their DX and you are not DX but most will polite respond to your signal. A typical response to a signal report such as I mentioned earlier is sending just two dots. In CW, sending two dots (technically the letter I but you are not sending an I) is sort of like a quick way to say "OK", or "I hear ya", or even "Bye" (which is a shortened version of "shave and a haircut, two bits").
If you are calling DX and someone answers who is not DX -- be polite. You should always know though if they are DX or not merely by their call sign. All separate DX entities are defined as having recognizable (usually) call signs. By usually, I mean it is not always easy to know unless you have the DX list in front of you to check. For example, in the US, Guantanamo Bay, Cuba, is DX (A US entity) but it's call sign prefix of KG4 can easily be mistaken for a QTH in the states representing the number 4 call area now that many call areas are using KG as a prefix in their sequentially assigned call signs.
The ARRL DX entity list can be found at:
ARRL DX CURRENT LIST
Not all DX is DX either. One example. I heard a strong DX station (CW) and planned to answer. I didn't recognize his call sign so I looked up the prefix on my ARRL DX Entity List poster hanging on the wall next to me. He was South Africa which is a particularly hard DX for my QTH. But, I listened to his CQ call again and this time heard his slash suffix -- he was operating remote in the state of Arizona. I answered anyway and we had a nice chat about his vacation visiting near the Grand Canyon. But, this QSO does not count as true DX for either him or I.