How is SWSD different from WHD?

SWSD is an SAAS whereas WHD is on premise

Yes, but is that the only difference?  Are there features that SWSD offers beyond what WHD does?

I think the biggest difference is the built-in Asset discovery/management. Most Help Desk/Service Desk needs to integrate a separate asset discovery tool. It also has a live chat feature which is pretty interesting.

At a glance this is what I could find.

SolarWinds Service Desk vs Web Help Desk - 2019 Feature and Pricing Comparison

Also,

Frequently Asked Questions | Support FAQ | Service Desk

Help Desk Ticketing Software - Asset Management | SolarWinds

Part of the trouble comparing feature sets between products is that superficially they may both "support" a feature but the specifics of how they did it may vary widely in terms of ease of use and the limitations around a feature. I'd expect that at some point once SW sales has some time to work with the implementation team formerly from Samanage they will cook up some comparisons between the two products, but it's probably going to be very 10,000 foot view and any meaningful comparison would probably require you to set up a real demo of the products side by side. 

If your current WHD setup is doing the job for you there may not be a pressing need to flip it over and start again.  Setting up a new service desk tool is always a big undertaking and there's a real opportunity cost in redoing what you have and then retraining everyone on the new procedures.  But if there are some specific gaps you are looking to address then I'd just shoot a list of them over to your account rep so they can do the leg work of figuring out if the new product addresses them or not.

At a glance this is what I could find.

SolarWinds Service Desk vs Web Help Desk - 2019 Feature and Pricing Comparison

Also,

Frequently Asked Questions | Support FAQ | Service Desk

Help Desk Ticketing Software - Asset Management | SolarWinds

Part of the trouble comparing feature sets between products is that superficially they may both "support" a feature but the specifics of how they did it may vary widely in terms of ease of use and the limitations around a feature. I'd expect that at some point once SW sales has some time to work with the implementation team formerly from Samanage they will cook up some comparisons between the two products, but it's probably going to be very 10,000 foot view and any meaningful comparison would probably require you to set up a real demo of the products side by side. 

If your current WHD setup is doing the job for you there may not be a pressing need to flip it over and start again.  Setting up a new service desk tool is always a big undertaking and there's a real opportunity cost in redoing what you have and then retraining everyone on the new procedures.  But if there are some specific gaps you are looking to address then I'd just shoot a list of them over to your account rep so they can do the leg work of figuring out if the new product addresses them or not.