If we develop some software in c# (or basically .Net), we don\'t install visual studio to any client. The client just have to have required .Net framework (1.0, 1.1, 2.0, 3.
If you use a SQL Server database to persist your data in your application you need
a. client-server infrastructure where your client connect to a central SQL Server via LAN
b. or use a client installed sql server edition (which is what you want I guess). For this you can use SQL Server Express edition or just a MSDE (Desktop Edition).
See for more details e.g. this blog post http://searchsqlserver.techtarget.com/tip/SQL-Server-2005-Express-vs-Desktop-Engine-MSDE or google for it, plenty of information from MS itself about MSDE.
EDIT: Since 2012 there is no more MSDE, but SQL Server 2012 Express brings a mode like MSDE did. See here: http://www.microsoft.com/sqlserver/en/us/editions/2012-editions/express.aspx
And as you can see here: http://www.microsoft.com/sqlserver/en/us/editions.aspx, there shouldn't be a function that you use that isn't available for a desktop application imho.
There is no client runtime required for database access besides the .NET framework installed (which you need for all .NET executables anyway).
If you want the database to reside on the same machine as the client free options would be e.g. SQL Server Express or SQLite.
OK let's back up a bit. Do you have a requirement for each of your software clients to have it's own local database? If this is the case there are far simpler ways of storing data on the client (I would suggest serialization to file as one approach).
If your requirement is to have each client connect through to a central database then you don't need any runtime components other than the .net core libraries.
Here are two ways for Windows Applications:
Desktop application that will be used by each clients separately without assigning a computer as server. You only need to install SSMS
and the application for your Clients. The Update/Delete/Insert operations will be done separately.
Client-Server Approach, install SSMS
and attach your DB on a computer. This computer will serve your clients as a server. Then install the exe file on any client computer, make sure the clients are connected to the server using the IP.