GFS is a cluster file system on Linux that allows servers to transparently access a single file system on a storage area network (SAN). Its highlights are performance and reliability (journaling filesystem, scalability through parallelism, etc).
LVM has become a part of the Linux kernel. It is a subsystem which allows arbitrary physical storage to be recognized as a virtual disk device. The physical storage can be remote, or it can even consist of multiple physical devices, but LVM abstracts those distinctions away from the operating system user. LVM also provides services for backing up data.