As I see it, a key distinction is that those involved in courtship have the specific intention of pursuing the possibility of marriage. That is, those who are able to marry and interested in marriage court as a process to validate that a particular person is a good spouse for them. The activities may be similar and they may refer to it as dating, but the intention creates a very different context.
Dating on the other hand, is a more casual activity, which is not necessarily intended to lead to a possible marriage, but may be intended as a means to romance, or fun.
In my opinion, certain types of dating, particularly when engaged in by those who are unable to marry for any reason or have no intention to consider marriage can be an occasion of sin. In other words, while not necessarily sinful in itself, it can introduce tempations that are better avoided.
Of course, courtship normally includes getting to know the family of the other person, especially the parents if they are living and nearby or in the same household. But if you are contemplating marriage it is only natural to wish to become aquainted with the other person’s family, whereas that may not be important for more casual socialization.