I think real postcard means a card that originally was of that size, meant to be that size (so not a part of something). And the size often about 4" x 6" or near it.
Sturdy enough, so cardboard/paperboard, not paper (so if you think a soft cover book, the material should be more of that of the cover, rather than the page, and not photo paper, or photo).
And usually artist info, what the postcard is about etc on the address side. I looked at your sent, and like the “North Dakota” one is such as most could think as “real postcard”. Also, instead of a view, it can have art in it. (Of course I don’t see if this is sturdy material and how the other side looks.)
Etsy then is so wide with quality, some sell “real postcards” that they bought in normal shop, like Moomin cards, some sell self printed images on somewhat thin papery material, and all between that.
So, if someone wants real postcards, I would send that above linked type, if I have such. Most likely that’s what they mean.
I have joined a swap, where one condition was to have a bar code, so it is sold as an item (no Temu/Ali Express box card), and is new enough, that was one weird requirement 
Here of course you are allowed to send for example self made cards to everyone, but in case someone cares to know what “real postcard” could mean.