SDxCentral has a piece on the current state of SD-WAN appliances. It distinguishes the three different forms SD-WAN can take (or at least for the purposes of their article). They divide the market-place into three segments. Thick, hybrid and thin appliances.
It doesn't matter which model is chosen; there will always be a physical appliance to convert the virtualised environment into the physical connections to the transport clouds.
The thick appliance is the capabilities of the traditional WAN stack condensed into a single device. It supports the functions of router, firewall, and WAN optimisation; as well as the SD-WAN capabilities of measurement, analysis and traffic steering. An example of this model is Cisco, with its IWAN deployment using ISR routers and their symbiotic nfv hosts.
The hybrid SD-WAN provides some capabilities in the cloud, like the virtualised appliances that support Amazon Web Services (AWS) and Microsoft Azure. It still uses some physical appliances at the client edge to provide the local connectivity to the various transports. This avoids the need to arrange a physical deployment either in the cloud itself (which is somewhat challenging) or at a point of presence close by. This is the Velocloud, Silver Peak and Nuage model, with a lightweight appliance which provides the capabilities on site, with some virtualised cloud appliances to support PaaS and SaaS deployments.
The thin appliance is really just a connection point to the transport clouds. These give just enough ability to connect and direct traffic and rely on the cloud to provide the additional services. This typically offers the connections between sites over a dedicated network, rather than the Internet. Aryaka is an example of this private-cloud model, as is Tata‘s IZO network.