Distributed filesystem - the generic term for a client/server or "network" filesystem where the data isn't locally attached to a host. There are lots of different kinds of distributed filesystems, the first ones coming out of research in the 1980s. NFS and CIFS are the most common distributed filesystems today
Global filesystem - this refers to the namespace, so that all files have the same name and path name when viewed from all hosts. This obviously makes it easy to share data across machines and users in different parts of the organization. For example, the WWW is a global namespace because a URL works everywhere. But, filesystems don't always have that property because your share definitions may not match mine, we may not see the same file servers or the same portions of those file servers.
AFS was an early provider of a global namespace - all files were organized under /afs/cellname/... and you could assemble AFS cells even from different organizations (e.g., different universities) into one shared filesystem. The Panasas filesystem (PanFS) supports a similar structure, if desired.
SAN filesystem - these provide a way for hosts to share Fibre Channel storage, which is traditionally carved into private chunks bound to different hosts. To provide sharing, a block-level metadata manager controls access to different SAN devices. A SAN Filesystem mounts storage natively in only one node, but connects all nodes to that storage and distributes block addresses to other nodes. Scalability is often an issue because blocks are a low-level way to share data placing a big burden on the metadata managers and requiring large network transactions in order to access data.
Examples include SGI cXFS, IBM GPFS, Red Hat Sistina, IBM SanFS, EMC Highroad and others.
Symmetric filesystems - A symmetric filesystem is one in which the clients also run the metadata manager code; that is, all nodes understand the disk structures. A concern with these systems is the burden that metadata management places on the client node, serving both itself and other nodes, which may impact the ability of the client to perform its intended compute jobs. Examples include Sistina GFS, GPFS, Compaq CFS, Veritas CFS, Polyserve Matrix
Asymmetric filesystems - An asymmetric filesystem is one in which there are one or more dedicated metadata managers that maintain the filesystem and its associated disk structures. Examples include Panasas ActiveScale, IBM SanFS, and Lustre. Traditional client/server filesystems like NFS and CIFS are also asymmetric.
Cluster filesystem - a distributed filesystem that is not a single server with a set of clients, but instead a cluster of servers that all work together to provide high performance service to their clients. To the clients the cluster is transparent - it is just "the filesystem", but the filesystem software deals with distributing requests to elements of the storage cluster.
Examples include: HP (DEC) Tru64 cluster and Spinnaker is a clustered NAS (NFS) service. Panasas ActiveScale is a cluster filesystem
Parallel filesystem - file systems with support for parallel applications, all nodes may be accessing the same files at the same time, concurrently reading and writing. Data for a single file is striped across multiple storage nodes to provide scalable performance to individual files. Examples of this include: Panasas ActiveScale, Lustre, GPFS and Sistina. NFSv4.1 will feature an extension to the NFS standard that supports parallel IO.
Finally, these definitions overlap. A SAN filesystem can be symmetric or asymmetric. Its servers can be clustered or single. And it can support parallel apps or not.
The Panasas Storage Cluster and its ActiveScale File System is a clustered (many servers share the work), asymmetric (metadata management does not happen on the clients), parallel (supports concurrent read and write well), object-based (not block-based) distributed (storage is across the network from clients) file system.