When designing the topology of a data model, does the database implementation matter? This application seems to be keeping data design separate from data storage. But I am curious if this even makes sense? 
If you click the code button you should be able to see clearly what question I am trying to ask. It outputs code for different databases, but shares the same model. What about the difference between SQL and NOSQL databases? https://www.schesign.com/o/examples/example_online_store/master/class/billinginformation
Without knowing anything about the project, yes it does make sense. It is true that different relational database management systems (RDBMS) may support different features. If a certain feature is particular to only a subset of all RDBMS's, then it's theoretically possible to either a) not support that feature when creating the model, b) abstract out the part of the feature that is common across all RDBMS's, or c) support the feature in the model but give an error when trying to convert the model to a sql script for an RDBMS that doesn't support the feature.

Relational databases ("SQL databases") are fundamentally very different from NoSQL databases. In fact, the entities NoSQL databases are largely unmodeled by design. I would be surprised if they add support for NoSQL databases, but then again I don't know anything about the project.