Integrated Security = SSPI

 The term Integrated Security = SSPI is a element in a connection string for an application to get access to a data source using a OLEDB or SqlClient provider. Usually it is just used because it is recommended by someone trustworthy.

SSPI is an abbreviation to Security Support Provider Interface which is a general implementation of the Generic Security Services Application Program Interface (GSSAPI). The interesting thing is that SSPI makes it possible to get the most secure authentication in a given context. In Windows it is at least a Kerberos or NTLM authentication. When possible you will get the more secure - and faster - Kerberos authentication. This is done by a negotiation, where some parameters like rank can be configured in Windows. The Windows configuration can be through Group Policies, both local and domain.

In relation to SSPI Kerberos and NTLM are Security Support Providers (SSPs) speaking Windows lingo. The documentation from Microsoft says that you can write our own SSP, but I couldn't find many details on the subject.

Speaking about Microsoft documentation the SSPI documentation as spred across Windows Server documentation on Windows Authentication with "Security Support Provider Interface Architecture" and Windows App Development on Remote Procedure Call (RPC) with "Security Support Provider Interface (SSPI)". In general I find it somewhat difficult to find documentation on the involved components in a login and authentication process.

Using SSPI is done with different parameters and values on each driver or provider.
With the SqlClient the keyword to the ConnectionString property is "Integrated Security" and the value is "SSPI" - which is „strongly recommended“ by Microsoft. Please notice that with SqlClient 5 the namespace is changed from System.Data.SqlClient to Microsoft.Data.SqlClient as the SqlClient component is removed from the .NET framework and is now available as a NuGet package.
With the ODBC driver the keyword is "Trusted_Connection" and the value is "Yes" which is an example on the big variations on both keywords and values. If you are using a driver from another vendor than Microsoft or a driver for another environment you should be very aware on these details as they can really bite you.