There are a couple different ways to determine this– if you are technically savvy you can right click on an e-commerce page (either catalog, checkout page, etc) and look at the source code.On many platforms you will find hints in the source code that will give you an idea what the site is running.
You can also look at the DNS/hosting information which would help figure out if the commerce solution is hosted/SaaS. Use InterNIC and enter the domain name. The results will return the nameservers which could point you in the right direction. If all that sleuthing seems too difficult, there’s an easier way. Try, Built With. It’s generally pretty reliable, as long as the system you're looking up isn’t custom/proprietary.