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Yeah, so the cost of the instance + software license is built in. The pay as you use cost includes the lic. cost for the product.
So, we could buy an instance and install our own version of SQL on it, or we could pay more for an instance type with SQL bundled on it already or we could use their SQL as a service RDS product.
You might need to look at specifics for your product but that's generally how it works.
Do you have the software? You can just spin up a vanilla instance and then install the software on it yourself and if you want to keep it around you can stop/start it and/or snapshot it and then bring up copies of it at a later date. (I think, I know nothing about your software, I just use AWS for serving web apps mostly)
If it's for one off stuff, you don't have to keep it around. But if you kill your instance you'll have to reinstall and copy your stuff to it every time. Storage costs are pretty cheap though (certainly compared to a running server)