Dating and seeing someone might seem like, as the same actions are being taken but with different intentions. One major thing that differentiates between these two terms is the intention. The intention of someone just going to see someone is different from the intention of someone going on a date. Someone dating another person, or going on a date with another person is also going to see the fellow, but the person is going to see someone is not necessarily dating the person he or she is seeing.
There are levels of human relationships. Dating is a more advanced level of relationship than seeing someone. Dating can lead to a more serious relationship and fidelity, but seeing someone does not really lead to an advanced level of relationship. You can see your family members such as your mum, dad, brother, sister, aunt, uncle, and cousin; but it is abnormal to date any of one's relatives.