What is the difference between OLE DB and ODBC data sources

You could call the SQLDataSources-function in ODBC32.DLL:

 using System.Runtime.InteropServices;
    public static class OdbcWrapper
    {
        [DllImport("odbc32.dll")]
        public static extern int SQLDataSources(int EnvHandle, int Direction, StringBuilder ServerName, int ServerNameBufferLenIn,
    ref int ServerNameBufferLenOut, StringBuilder Driver, int DriverBufferLenIn, ref int DriverBufferLenOut);

        [DllImport("odbc32.dll")]
        public static extern int SQLAllocEnv(ref int EnvHandle);
    }

Example that lists the Data Sources:

public void ListODBCsources()
    {
        int envHandle=0;
        const int SQL_FETCH_NEXT = 1;
        const int SQL_FETCH_FIRST_SYSTEM = 32;

        if (OdbcWrapper.SQLAllocEnv(ref envHandle) != -1)
        {
            int ret;
            StringBuilder serverName = new StringBuilder(1024);
            StringBuilder driverName = new StringBuilder(1024);
            int snLen = 0;
            int driverLen = 0;
            ret = OdbcWrapper.SQLDataSources(envHandle, SQL_FETCH_FIRST_SYSTEM, serverName, serverName.Capacity, ref snLen,
                        driverName, driverName.Capacity, ref driverLen);
            while (ret == 0)
            {
                System.Windows.Forms.MessageBox.Show(serverName + System.Environment.NewLine + driverName);
                ret = OdbcWrapper.SQLDataSources(envHandle, SQL_FETCH_NEXT, serverName, serverName.Capacity, ref snLen,
                        driverName, driverName.Capacity, ref driverLen);
            } 
        }

    }

The first call to SQLDataSources with SQL_FETCH_FIRST_SYSTEM tells the function to start the listing with the System-DSNs. If you simply started with SQL_FETCH_NEXT it would first list the drivers. Link to the function ref on Microsofts site

Edit:
Everybody seems to know it but I just found out yesterday when I used this code in a new poject: if you are compiling this with VS on a 64 Bit Windows you have to set the "Target Platform" to "x86" or the code won't run.

ODBC is a C API for accessing databases. There is a standard for it, it is supported by every major database vendor, it is very well documented, it is cross-platform. OLEDB is a similar interface that uses Microsoft's COM technology instead of the C API. This means that it is only easily useable on platforms that support COM.

At the end of the day, both libraries provide roughly equivalent basic functionality. Indeed, Some OLEDB drivers actually make use of ODBC rather than native database libraries.

So, if you are C# developer, working on Windows, OLEDB is the obvious choice between the two. If you are using C (or C++ not using COM), or need cross-platform support, then ODBC is the better bet.