A few last months constantly I see misunderstanding what Business Central SaaS offering is. To be honest I thought it is all well known, but often it is not a case. Because of that, I’ve readjusted standard IaaS vs PaaS vs SaaS chart and made it applicable to Business Central. I think this chart speaks for itself, but if someone needs additional info, you can send a question and I’ll add details.

Just to be clear, on the top level where we have Company Data, I think on using BC as a system through UI or API’s. That means you are master of your data. You need to be sure how you enter and post your documents. But if we talk about configuration of system, mostly it will be done by your partner, but again this is your decision (as customer) to find trusted partner to work with.
As this chart cannot offer completely picture, I’ve added one more. First one was all about technology, but the next one is about licensing and what is included in system.

*) One thing maybe not 100% clear from this chart is infrastructure subscription if you are using BC on Azure (IaaS model). If you want to use Business Central deployed on Azure infrastructure (no SaaS), you can use a few different models. First you (as customer) can have your own infrastructure (1 VM, 2 VM’2, or VM + Azure SQL). The second, you (as customer) can use partner infrastructure and in this case you can dedicated hardware or services to you (as if you use your own) or you can use shared resources (more cost effective). In this case, middle tier can be used for more clients, as well as Azure SQL database can be added to Azure Elastic Database Pool and to get better performances and better cost. You can find ideas how to make it here (and this is important especially if BC SaaS is not available in your country). And one more thing… if you are using model BC on Azure, cost for OS and SQL Server is included in HW Subscription.
I hope it is now far clearer, but again if you need any additional detail, just send a question.