I'm never sure how to illustrate the difference between the observable universe and the visible universe, as both have a radius of 13.7 billion light years (light travel time).
The visible universe is represented by all the photons we receive currently, but what does that actually represent?
We see the stars in our galaxy, other galaxies and the CMBR (and a few other things). We see light that was emitted up to 100,000 years ago, in our galaxy. We see the light from Andromeda, emitted around 2.5 million years ago. We see galaxies at increasing distances, whose light has been travelling for longer and longer. We infer that those galaxies were receding from us at the time, with a speed that increases with distance.
We see galaxies whose light has been travelling for 9 billion years. They were 5.7 billion light years away at the time and were apparently receding at the speed of light. We see galaxies whose light has been travelling for nearly 13 billion years, but these galaxies were only 3.5 billion light years away when they emitted that light. They were apparently receding faster than light at that time.
We see the CMBR, the light that has been travelling for 13.7 billion years and was originally emitted at a distance of only around 40 million light years away.
Trying to take all that and condense it into a model that you can visualise is a little difficult. The radius, if it has one, is as you say 13.7 billion light years, but that is purely in terms of light travel time. In terms of distance, the furthest objects visible are galaxies at redshift z=1.4, with an angular diameter distance of 5.7 billion light years, the galaxies that were receding at c when they emitted their light.
Those galaxies are supposed to be around 13.7 billion light years away today, but that is a co-moving distance so it really applies to the observable universe. In our visible universe those higher redshift galaxies have co-moving distances of up to 30 billion light years, and the CMBR with a co-moving distance of 46 billion.
It is difficult to meaningfully describe a past light cone for an expanding universe, the visible universe. I usually say "everything we can currently see" but that is hard to get a real grasp of. The visible universe is everything we can see, the observable universe is whatever has happened to those regions of the universe, since. The visible universe is the contents of our past light cone, the observable universe is where the coordinates that were within our past light cone have receded to since. The actual universe is probably larger.
The map at the atlas of the universe, which says it is of the visible universe, is actually a representation of the observable universe, which doesn't help.
I have also seen the visible universe described as everything within our Hubble sphere. Here, we consider only objects with recession speeds below c as visible. If we consider the angular diameter distance (where the Hubble sphere was), it was 5.7 Glyr away, 9 billion years ago, but those galaxies are now 13.7 billion Glyr away.
Then there is the future of our past light cone! It is limited by the cosmological event horizon, currently 16 billion light years away. With this definition, our future visible universe is represented by all the light we have, or will ever, see. Our future observable universe is a lot simpler as it is always the particle horizon!
The "visible" universe is a complicated creature!