>>>Hi,
>>>
>>>I would to make sure that I am using the correct terms when writing to a customers. I need to write to them that they need to install a SQL Server on the application server or set up a SQL Instance with SSMS on the application server. My understanding is that "SQL Instance" would mean that the SQL Server is installed on another server with me being able to attach my application database to this SQL Instance.
>>>Do I understand the "SQL Instance" term correctly?
>>>
>>>TIA
>>
>>No, your understanding is wrong. You can install several SQL Server "instances" on the same server. You can only install one default instance and other installations will have to use some name for SQL Server.
>>
>>That's all what's in the term.
>
>So would I describe that I need to have a SSMS on application server "pointing" to the SQL Server installed on another server?

You need to have SSMS installed and need to be able to connect to the installed SQL Server (on the server).