SSDT, SSDT-BI confusion in backwards compatibility for different SQL version

问题

After extensively searching over google about SSDT and SSDT-BI for different SQL Server versions, I would like someone to pin-point differences and clear my messed up thoughts !

Aim: To upgrade SSIS packages from sql server-2012 to sql server-2014.

Originally build from: build on SSDT-BI 2010 Shell(Integrated) which were deployed on SQL Server 2012 Enterprise edition.

Now I need to deploy them on SQL Server 2014 Developer edition (for test purpose).

I have successfully installed SSDT-BI 2013 Shell(Integrated) and SSDT 2015 Shell(Integrated).

Problem:

When I open my package in 2013, it prompts for Package Upgrade wizard(which later on fails to upgrade), but 2015 doesn't give any such prompt (why?). It simply opens. I understand that this is because, we can choose Deployment Target Version in 2015 and 'package upgrade' is done in 2015 when actually deploying at any version. So am I right?
I thought SSDT 2015 was meant to be only for SQL Server 2016 and not earlier versions. So, am I right to assume that SSDT 2013 can be used with SQL 2012 ?
2015 Shell(Integrated) is SSDT or SSDT-BI? What's the difference in it?

What I understand:

- SQL 2012 : SSDT-BI 2010 Shell Integrated
- SQL 2014 : SSDT-BI 2013 Shell Integrated
- SQL 2016 : SSDT 2015 Shell Integrated
Backwards compatibility of SQL 2016. ie Packages created in SSDT 2015 can be deployed on 2016,2014,2012.

I would appreciate someone answering point by point and clear the confusion. Definitely, there is some pointers, which I don't understand fully.

Cheers.

ps: This blog was helpful while figuring things.

回答1:

First and Second problem

If you check this Microsoft article, then you will see that SSDT 2015 can be used with SQL Server 2012+, but SSDT 2013 is only used with SQL Server 2014

Third problem

If you refer to this Artcile:

In SSIS 2012 , 2013:

Because of confusion with the database tools in Visual Studio (also called SSDT), the templates were renamed to SQL Server Data Tools for Business Intelligence (SSDT-BI).

In SSIS 2015 :