Can you tell me the difference between courting a
gentleman and dating one?

That's the part I'm having trouble with.
I hope no one thinks I am intentionally trying to be difficult here. It's just that I hear these words tossed around a lot and no one ever seems to really know. I think I'll do some googling haha
I'll explain from the traditional perspective. Keep in mind what I said about there being a lot of variety depending on generation and culture, and also that even today there are modern reincarnations of courtship.
It is the gentleman who courts the lady, and not the other way around. He initiates, but not before receiving permission from an authority figure (or just someone who was looking out for her best interest). This was often her father, but in other circumstances it could also be another relative, a good friend, a mentor, a pastor, etc. This person would hold the gentleman accountable to the highest standards of purity and honor during the time he was courting the lady. During that time, the gentleman and lady would get to know one another, but always under the watchful eye of the person holding him accountable. Courtship was different than arranged marriages, as the "courting" means he is trying to win her heart. If it became clear to the the authority figure that this man was worthy of the lady, the blessing would be given and it is the lady who makes the final decision.
All that said, in the context of a modern dating relationship, if the man is a true gentleman (and marriage minded), there is not much difference, aside from the level of accountability and the amount of boundaries. Courtship usually implies minimal time spent alone together, where dating is more flexible. In the case of a grown woman who does not have parents available/around to hold a suitor accountable, I would think it would be rare for a man, even a gentleman to seek out the blessing and approval of her pastor/mentor/friend/brother/etc. before dating her. However, in courtship, this would be expected.
Note: I'm just explaining this from a traditional, historical perspective. I'm not trying to connect any of this with biblical examples.
