The kubernetes pods share ipc and network namespaces (and pid soon). You may be referring to mount namespace by volumes namespace. The mount namespace is the minimum that distinguishes one container from the other as that's the mean by which they see different file-system hierarchies created from their images.
k8s volumes are bind mounted into the containers in a pod.
I wasn't sure if pods shared mount namespace or just the external volumes. It sounds like the same external volumes are mounted in each container but the rest of mounts are different.
k8s volumes are bind mounted into the containers in a pod.