Not really. For instance NVIDIA released day 1 Vulkan extensions for their new raytracing and neural net tech (VK_NV_cluster_acceleration_structure, VK_NV_partitioned_tlas, VK_NV_cooperative_vector), as well as equivalent NVAPI extensions for DirectX12. Equal support, although DirectX12 is technically worse as you need to use NVAPI and rely on a prerelease version of DXC, as unlike Vulkan and SPIR-V, DirectX12 has no mechanism for vendor-specific extensions (for good or bad).
Meanwhile the APIs, both at a surface level and how the driver implements them under the hood, are basically identical. So identical in fact, that NVIDIA has the nvrhi project which provides a thin wrapper over Vulkan/DirectX12 so that you can run on multiple platforms via one API.