Modern graphics engines are based on shaders. Shaders are programs that run on graphics hardware to produce geometry (the scene), images (the rendered scene), and then pixel based post-effects.
From the Wikipedia article on shaders:
Shaders are simple programs that describe the traits of either a vertex or a pixel. Vertex shaders describe the traits (position, texture coordinates, colors, etc.) of a vertex, while pixel shaders describe the traits (color, z-depth and alpha value) of a pixel. A vertex shader is called for each vertex in a primitive (possibly after tessellation); thus one vertex in, one (updated) vertex out. Each vertex is then rendered as a series of pixels onto a surface (block of memory) that will eventually be sent to the screen.
Modern graphics cards have between hundreds and thousands of computational cores that are capable of executing these shaders. They used to be split between geometry, vertex and pixel shaders but the architecture is now unified, a core is capable of executing any type of shader. This allows a much better use of resources as a game engine and/or graphics card driver can adjust how many shaders get apropriated to which task. More cores allocated to geometry shaders can give you more detail in the landscape, more cores allocated to pixel shading can give better after effects such as motion blur or lighting effects.
Essentially for every pixel you see on the screen a number of shaders are run at various levels on the computational cores that are available.
CUDA is simply Nvidias API that gives developers access to the cores on the GPU. While I have heard the term "CUDA core", in graphics a CUDA core is analogous to a stream processor which is the type of processing core that the graphics cards use. CUDA runs programs on the graphics cores, the programs can be shaders or they can be compute tasks to do highly parallel tasks such as video encoding.
If you turn down the level of detail in a game you can feasibly reduce the computational load on the graphics card to a point where you can use it to do other things, but unless you can tell those other tasks to slow down as well then they are likely to try and hog the graphics processor cores and make your game unplayable.
I can confirm that the 3000 series, and presumably older RTX and GTX cards still have cuda cores, in addition to tensor and RT cores.
You can check the CUDA core count from the nvidia control panel, under system information
The RTX 3080 for example has 8704 CUDA cores listed
If you don't have the exact card on hand, there's lists you can use to look it up. WCCFtech has specifications for some newer, and some speculative cards. For the models that are currently out as of Oct 2020, the numbers look correct, though
Best Answer
In layman terms, CUDA Cores and Stream processors are exactly the same. The question is similar to asking whether Intel and AMD CPUs are the same or not. The difference in names is mostly commercial branding.
Both NVIDIA and ATI/AMD cards are multi-core units excelling in executing parallel programs.
The difference is that AMD stream processors are smaller, simpler, and run on lower frequency. NVIDIA CUDA cores are bigger, more complex and run on a higher frequency. That's why one cannot judge by the number of processors.
Both cards use different architectures, where CUDA are more general-purpose. This difference also shows in the way programs are compiled to run on these cards. The CUDA compiler does less optimization, letting the card assign the cores as needed at runtime, while the AMD compiler optimizes much more as regarding core assignments.
Another difference is developer support, where NVIDIA does a much bigger effort to woo developers to their cards. This is why there are many more libraries, code snippets and developer resources in general available for NVIDIA.
The effect of this difference in architecture depends on the task to do, and whether a greater number of processors, although slower ones, improves the performance or not. For example, AMD cards are much better for Bitcoin mining. For graphics, the comparison usually comes up as a close match for similarly-priced cards.