Vulkan is an open-source, cross-platform 3D graphics and compute API that provides access to modern GPUs (graphics processing units). It's designed to provide a low-overhead, cross-platform 3D graphics and compute API that can be used to power games, engines, and other 3D applications. Vulkan is designed to provide efficient, high-performance access to modern GPUs on a wide range of platforms, including Windows, Linux, macOS, iOS, and Android. It supports a wide range of graphics and compute features, including advanced render passes, instanced draws, compute shaders, and more. With Vulkan, developers can target many different types of hardware, including mobile GPUs, discrete GPUs, integrated GPUs, and more. Vulkan also provides developers with improved performance, scalability, and flexibility compared to other 3D graphics APIs.
SDL handles everything (input, sound, files) and wraps graphics APIs like Vulkan. It is not the same.