Provisioning storage is a basic public cloud feature. The provisioned virtual storage is provisioned off the local system, and off the LAN, thus is also an online storage.
(But online storage can be hosted on a cloud or using legacy technologies.)
Online storage refers to the fact that something is not local, but accessible thru a connection, here via the Internet. How data are then actually stored is not part of the online concept, and neither is the protocol used to access remote data. As soon as data are stored off the local computer, we can talk about online storage, especially if this is also off the LAN (else "network storage" is more usual).
Some points of reference about cloud computing
There isn't (yet) an agreed definition for what is cloud computing. Cloud is still basically a marketing word, barely a new concept. Some previously known mechanisms are typically used for the cloud concept: virtualization of CPU, RAM, storage and network, and clustering. VMWare is a good example of resource virtualization manager on x86 platforms (the name often used is hypervisor). Long before VMWare, IBM invented VM-CP which has the same intent.
Physical storage can be virtualized using a storage hypervisor.
An hypervisor can be configured to manage multiple physical resources (CPU, RAM, storage, network) on different physical platforms, even different LANs.
As soon as everything is virtual, then it is easy to create copies of virtual machines, virtual networks and virtual storage. It is also easy to create virtual resources on a pool of physical resources. Easy duplication allows for implementing quick backup, and restoration of a stored virtual resource is possible on another hardware under the control of the supervisor. This allows in turn to move virtual resources between the physical systems of the pool in case one goes down or is overloaded.
Creating a new resource can be done from an image of a machine (with predefined OS, middleware, and applications). Different images can coexist to create different virtual resources. Depending on what is part of the image, there are simple virtual machines without OS, with OS, with OS and middleware, with OS, middleware and applications, etc. Virtual machines are commonly referred by their somehow agreed types: IaaS, PaaS, SaaS (infrastructure, platform, software... as a service). Typically these resources are rented for a monthly fee to public (shared) or private (dedicated) cloud providers and paid "as a service" as long as they are used.
Creating resources can be done using a simple interface, typically a web page, and the management of the virtual resources can be delegated to the end user. Creating a new virtual resource is called "provisioning".
Today using a cloud commonly refers to the capability for the user to provision resources that exist on one or several physical platforms across a LAN or a WAN.
The idea that when it is "on the cloud" then you cannot know exactly where it is, because it is moving depending on current system load and failures, is not exact. Many forms of cloud solutions for enterprises are typically implemented on dedicated hardware (e.g. private clouds located somewhere, sometime just hosted in the enterprise premises and connected to the LAN.