Painted or printed backdrop?
The difference is not colour. It is how the surface behaves in light.

Surface
A printed backdrop is even. The colour is the same everywhere, because it was printed. Painted canvas is not even anywhere: it has darker and lighter areas, and the trace of how the paint was laid down. In a photograph this reads as depth, and it is there before you have moved a single light.
The same works in reverse. If you need a genuinely uniform surface, for product shots or passport photographs, a painted backdrop is the wrong tool. It is made to be seen, not to disappear.
No banding
An even paper backdrop produces a very slow tonal gradient as the light falls off towards the edges. A digital image has a limited number of tonal steps, and compression reduces them further. When the gradient is slower than the gap between the steps, curved contour lines appear instead of a smooth transition. That is banding.
Sensor noise usually hides it. When the image is scaled down for the web the noise averages away and the lines show up. That is when they get noticed.
Painted canvas has variation of its own, and it is coarser than noise. It survives downscaling and keeps breaking up the gradient, so the bands do not form.
This is the difference that does not show in the studio but in post. It is work you do not have to do.
Light
Vinyl and many printed backdrops are somewhat glossy. Gloss means reflections: a flash leaves a bright patch that you either light away or retouch afterwards. Painted canvas is matte, so it does not produce the same reflections.
A painted surface also responds to the direction of light. Light from the side strengthens its variation and light from the front evens it out, so the same canvas can look different in two photographs.
Durability
A paper roll is a consumable. It tears, it gets dirty, it runs out, and every shoot takes a piece of it. Vinyl survives wiping but creases and scratches.
Painted canvas is made to be used for years. Folds relax as the canvas hangs, and the surface takes being moved around a studio. There is a separate guide on storing and straightening it.
What if the background is added afterwards?
A third option is to buy no backdrop at all and add the background in post. That is a real alternative, and it deserves a straight answer.
The light from a physical backdrop is real light. It falls on the subject, reflects into skin and clothing and colours the edges of the hair. A background added afterwards does none of that, so the light has to be rebuilt, and that is where a composite usually gives itself away.
Edges are the other difference. Hair, fur, veils and sheer fabric are exactly where masking takes time and shows. With a painted backdrop there is nothing to mask.
The third is time. A backdrop is bought once and used for years, while retouching costs hours per image. The result is also there in camera, so the client can approve it at the shoot rather than a week later.
Compositing wins when you need a place you cannot get to, an exact brand colour, or the same shot on several different backgrounds.
Which one to choose
A printed backdrop makes sense when you need one exact colour, when the backdrop is going to be removed in post, or when budget decides.
A painted backdrop makes sense when the backdrop is part of the picture. In portraits, fashion, musicians and animals it does work on behalf of the image instead of being empty space behind the subject.
Ask about the backdrops
If something is still open, send me an email. I would rather answer a question than sell you the wrong backdrop.