I am facing an issue with the SSDP (Simple Service Discovery Protocol) to discover the devices on the same local network but on different subnets.
Can I do that to discover the devices that are on the different subnets with the WSD (Web Service Discovery) method?
What are the differences between SSDP and WSD?
On IPV4 networks, SSDP and WSD broadcast to 239.255.255.250. That is not a routable address (so it doesn't work 'on the internet'), but it's also not part of any of your subnets. So, either your devices see multicast broadcasts, or they don't, and either they reply or they don't, and nothing in the two protocols says anything about that.
If you are having problems with subnets, that suggests to me that unicast replies are not traversing the subnet gateway. That's not likely to be fixed by changing protocols.
Both protocols can also use IPV6 broadcast addresses, and the principles are the same.
SSDP was a binary protocol: WSD was a later XML (SOAP) protocol. MS has since moved on to another, even more complex discovery protocol. Because it was more recent, WSD supports some kind of encrypted channel: as far as I know, SSDP does not.