When an application writes a file, the filesystem translates that into a set of block writes addressed by Logical Block Address (LBA). The request travels over a protocol to the storage device. Locally that is SATA, SAS, or NVMe. Across a network it is iSCSI, Fibre Channel, or NVMe over Fabrics, where blocks move over TCP or a dedicated fabric to a remote array.
In the cloud the volume is virtual. Amazon EBS, for example, presents a volume that looks like a local disk to your EC2 instance, but the blocks actually live on a replicated storage backend reached over the network. The instance sees a normal /dev/xvdf device and has no idea the bytes are elsewhere.
Performance is measured in IOPS (input/output operations per second), throughput in MB/s, and latency in milliseconds or microseconds. A local NVMe SSD can hit hundreds of thousands of IOPS at sub-100-microsecond latency. A network-attached EBS gp3 volume gives a baseline of 3,000 IOPS and 125 MB/s, and you can provision up to 80,000 IOPS and 2,000 MB/s per volume.