CUDA has 2 primary APIs, the runtime and the driver API. Both have a corresponding version (e.g. 8.0, 9.0, etc.)
The necessary support for the driver API (e.g. libcuda.so on linux) is installed by the GPU driver installer.
The necessary support for the runtime API (e.g. libcudart.so on linux, and also nvcc) is installed by the CUDA toolkit installer (which may also have a GPU driver installer bundled in it).
In any event, the (installed) driver API version may not always match the (installed) runtime API version, especially if you install a GPU driver independently from installing CUDA (i.e. the CUDA toolkit).
The nvidia-smi tool gets installed by the GPU driver installer, and generally has the GPU driver in view, not anything installed by the CUDA toolkit installer.
Recently (somewhere between 410.48 and 410.73 driver version on linux) the powers-that-be at NVIDIA decided to add reporting of the CUDA Driver API version installed by the driver, in the output from nvidia-smi.
This has no connection to the installed CUDA runtime version.
nvcc, the CUDA compiler-driver tool that is installed with the CUDA toolkit, will always report the CUDA runtime version that it was built to recognize. It doesn’t know anything about what driver version is installed, or even if a GPU driver is installed.
Therefore, by design, these two numbers don’t necessarily match, as they are reflective of two different things.
If you are wondering why nvcc -V displays a version of CUDA you weren’t expecting (e.g. it displays a version other than the one you think you installed) or doesn’t display anything at all, version wise, it may be because you haven’t followed the mandatory instructions in step 7 (prior to CUDA 11) (or step 6 in the CUDA 11 linux install guide) of the cuda linux install guide
Note that although this question mostly has linux in view, the same concepts apply to windows CUDA installs. The driver has a CUDA driver version associated with it (which can be queried with nvidia-smi, for example). The CUDA runtime also has a CUDA runtime version associated with it. The two will not necessarily match in all cases.
In most cases, if nvidia-smi reports a CUDA version that is numerically equal to or higher than the one reported by nvcc -V, this is not a cause for concern. That is a defined compatibility path in CUDA (newer drivers/driver API support “older” CUDA toolkits/runtime API). For example if nvidia-smi reports CUDA 10.2, and nvcc -V reports CUDA 10.1, that is generally not cause for concern. It should just work, and it does not necessarily mean that you “actually installed CUDA 10.2 when you meant to install CUDA 10.1”
If nvcc command doesn’t report anything at all (e.g. Command 'nvcc' not found...) or if it reports an unexpected CUDA version, this may also be due to an incorrect CUDA install, i.e the mandatory steps mentioned above were not performed correctly. You can start to figure this out by using a linux utility like find or locate (use man pages to learn how, please) to find your nvcc executable. Assuming there is only one, the path to it can then be used to fix your PATH environment variable. The CUDA linux install guide also explains how to set this. You may need to adjust the CUDA version in the PATH variable to match your actual CUDA version desired/installed.
Similarly, when using docker, the nvidia-smi command will generally report the driver version installed on the base machine, whereas other version methods like nvcc --version will report the CUDA version installed inside the docker container.
Similarly, if you have used another installation method for the CUDA “toolkit” such as Anaconda, you may discover that the version indicated by Anaconda does not “match” the version indicated by nvidia-smi. However the above comments still apply. Older CUDA toolkits installed by Anaconda can be used with newer versions reported by nvidia-smi, and the fact that nvidia-smi reports a newer/higher CUDA version than the one installed by Anaconda does not mean you have an installation problem.
Here is another question that covers similar ground. The above treatment does not in any way indicate that this answer is only applicable if you have installed multiple CUDA versions instentionally or unintentionally. The situation presents itself any time you install CUDA. The version reported by nvcc and nvidia-smi may not match, and that is expected behavior and in most cases quite normal.