Maybe we need a new classification of these as the new fangled yoyos. I do sometimes have the fabric meet in the middle. It just isn't my first priority.
I cut a fabric circle. I then run a thread around the circle. With a template I then pull the fabric into a circle with a hole on one side. At this point the "Yoyo" I made and your yoyo are the same.
Then I take out the template. Before I use my yoyo it is the same as yours. The only differance is I used a template to get a good circle shape.
I don't cut a perfect circle just because it is a time saver not to. I have the template instead to create the shape. Same differance. I need a more accurate circle to make the DP blocks. The ones in the directions I saw were not good circles when finished. Tho they began with a perfect 4" circle.
If I cut a large enough fabric circle I will have a yoyo that is the same on both sides with a tiny hole in one side. With the bulk. I cut mine randomly by eye.
After you get done with your yoyos you choose to sew them together into a quilt or project.
I use mine to sew onto a background square. Up to this point the yoyos are the same.
I just choose to use mine to make Drunkard's Path blocks by sewing them onto a background and cutting it into 4 pieces. Then I trim because I don't like the thickness. But you don't have to trim. It can stay the way it is.
The definitive thing for me in this is I could take your yoyo and sew it onto a background square and cut into 4 and trim and you would not know which one was my yoyo or yours.
How I use the yoyo is not the definition of a yoyo. I use them to add to a square. The traditional is is to sew them together. But the yoyos are still the same thing no matter how you use them.
Knowing I am going to trim them later I usually make the circles smaller than you do. But the steps are still the same. In the end the yoyos look the same. I have just cut back on the size of the underside to accomadate this project.